{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to size your bets - The Kelly Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "he Kelly rule has a long history in gambling because it provides guidance on how much to stake on each of an (infinite) sequence of bets with varying (but favorable) odds to maximize terminal wealth. It was published as A New Interpretation of the Information Rate in 1956 by John Kelly who was a colleague of Claude Shannon's at Bell Labs. He was intrigued by bets placed on candidates at the new quiz show The $64,000 Question, where a viewer on the west coast used the three-hour delay to obtain insider information about the winners. \n",
    "\n",
    "Kelly drew a connection to Shannon's information theory to solve for the bet that is optimal for long-term capital growth when the odds are favorable, but uncertainty remains. His rule maximizes logarithmic wealth as a function of the odds of success of each game, and includes implicit bankruptcy protection since log(0) is negative infinity so that a Kelly gambler would naturally avoid losing everything."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:27.877055Z",
     "start_time": "2018-10-30T23:49:27.616904Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from sympy import symbols, solve, log, diff\n",
    "from scipy.optimize import minimize_scalar, newton, minimize\n",
    "from scipy.integrate import quad\n",
    "from scipy.stats import norm\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import dirichlet\n",
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:27.964848Z",
     "start_time": "2018-10-30T23:49:27.952834Z"
    }
   },
   "outputs": [],
   "source": [
    "warnings.filterwarnings('ignore')\n",
    "plt.style.use('fivethirtyeight')\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The optimal size of a bet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kelly began by analyzing games with a binary win-lose outcome. The key variables are:\n",
    "- b: The odds define the amount won for a \\\\$1 bet. Odds = 5/1 implies a \\\\$5 gain if the bet wins, plus recovery of the \\\\$1 capital.\n",
    "- p: The probability defines the likelihood of a favorable outcome.\n",
    "- f: The share of the current capital to bet.\n",
    "- V: The value of the capital as a result of betting.\n",
    "\n",
    "The Kelly rule aims to maximize the value's growth rate, G, of infinitely-repeated bets (see Chapter 5 for background).\n",
    "$$G=\\lim_{N\\rightarrow\\infty}=\\frac{1}{N}\\log\\frac{V_N}{V_0}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can maximize the rate of growth G by maximizing G with respect to f, as illustrated using sympy as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:28.591420Z",
     "start_time": "2018-10-30T23:49:28.317222Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(odds*probability + probability - 1)/odds]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "share, odds, probability = symbols('share odds probability')\n",
    "Value = probability * log(1 + odds * share) + (1 - probability) * log(1 - share)\n",
    "solve(diff(Value, share), share)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:29.177068Z",
     "start_time": "2018-10-30T23:49:29.127374Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2*p - 1]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f, p = symbols('f p')\n",
    "y = p * log(1 + f) + (1 - p) * log(1 - f)\n",
    "solve(diff(y, f), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get S&P 500 Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:42.572206Z",
     "start_time": "2018-10-30T23:49:42.551483Z"
    }
   },
   "outputs": [],
   "source": [
    "with pd.HDFStore('../../data/assets.h5') as store:\n",
    "    sp500 = store['sp500/prices'].close"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Returns & Standard Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:43.938295Z",
     "start_time": "2018-10-30T23:49:43.905336Z"
    }
   },
   "outputs": [],
   "source": [
    "annual_returns = sp500.resample('A').last().pct_change().to_frame('sp500')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:45.879741Z",
     "start_time": "2018-10-30T23:49:45.875845Z"
    }
   },
   "outputs": [],
   "source": [
    "return_params = annual_returns.sp500.rolling(25).agg(['mean', 'std']).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:46.120190Z",
     "start_time": "2018-10-30T23:49:46.100280Z"
    }
   },
   "outputs": [],
   "source": [
    "return_ci = (return_params[['mean']]\n",
    "                .assign(lower=return_params['mean'].sub(return_params['std'].mul(2)))\n",
    "                .assign(upper=return_params['mean'].add(return_params['std'].mul(2))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:46.611142Z",
     "start_time": "2018-10-30T23:49:46.302209Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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oOc4RQgghhDhRzp67wU9glq7sHcEcKmWYWIdHUAMXlAV2ESpnKvbUdxBf+WPip30Pe+L5oyL5hFeSSPxknx6nh/t/Gv0UIDrSKyOozx5zPyGEOBYZAR1mZsE8rAlvwKt9DGfnT4kt+VK2QxJCCCFGvaD7IF71Q4BBZNblaTlnZP5nw9lKZhyMCEqptJw3m8yyleEoZuMzWKUr0IFH0L49fK3gOAlo6Urcvb/Gq34Iv+n5MPE2oxg5k4nMugIVKRyOtyCEGOVkBDQL7FmXgxHFb3hiSE2uhThZ7sE/knj+Krz6J9BaZzscIYQ4ac6un4P2sarehJE3PS3nVEqhIkUoMzomkk8Ie3oC+I1r0VoTdO6GIIXKmXTcBNIomIuRNwMCF504RNC5i6BtC17NX0ht/S5aB8PxFoQQo5yMgGaBES3DnvZu3D2/JLX1+5hFi4CeX2xWHHvS2zByp2Y1RjF2aR3g7LkL3HZSbZswChcSmf1RzML52Q5NCCGGJOjcjd/wBBhR7JkfyHY4I5qRPwcVKUanGgg697yy/rNg4PWfhyllEFtxK9ppBj+JDpLgdpDc9M2wRcuB+7GnviPTb0EIMcpJApol9tR34FU/gk7W4NX2XQvqHXoIe8b7sae+c8BqdEIMVdC5C9x2sPJAmQRtW0g+/xnM8nMwcqeA1kD4xyhchFl6xph58i+EGJu8pucBsCpfjxEty3I0I5tSBmbpGXg1j+A3PkPQtQ/ov/9nv8cbJipW3mdbdMHnSG38Cs6un2EULcYsmJf2uIUQY4dkN1mizBix5d/Bb90I6PB+H03Qugmv9q+4u3+O3/AEkfmfw8zvvyeXEEPhN28AwCp/DZE5H8Xddy/ugfvCKeENR+9vFMwnMvNDmCXLhjlSIYQ4MUFPQR2zWL6nToRZtjJMQJvWolPN4bbjFCA6Fqv8LPzJF+Md/AOpTd8ifsatKCs3XeEKIcYYSUCzyIhPwIhP6Ltx4vlYE84jte1mgo6dJNd9ksj8z2JXvTE7QYoxx29eD4BZcirKyiUy60NYky7Aq/s7BA6gQBngJ3GrHyZo30Zyw7UYxcuwp74DI3caKlqKUmY234YQQgCgAx+/dTMARvGSLEczOpgly8GwCdpfDjdYuaiTXPoTmX0FQesmgs5dpF7+b6ILvwBeF9ppQqdaULlTMaIlaYheCDHaSQI6Apkly4mf8SOcnT/Bq/4z7r7fSAIq0kL7KYK2TUDfkQIjVk5k2ruO2t+e9h7cg3/A3f9bgpYNpFrC0VOUhYpVYuROIzJvNUa0dFjiF0KIVws6d4LfjYpPlOm3J0iZMcziZfhNzwFh9duT6ZkKoIwI0UXXklj3Sfy6v9Pd8FTPQ82e13MmE1/5E1nSIYSQKrgjlbLiROZ+HAwb3X0Q7XZkOyQxBgRtmyFwMfJmoSJFx91fWXEi099Lzlk/x57+fozChahICWgPnTiE3/gUXs1fhyFyIYTo3+Fq8maRjH4Ohlm6sve/j9f/80QZuVOIzvsUoMLk04yjciaBEQ3vZXrWmwohxjcZAR3BlGFj5M0maN+K374dq/S0bIckRrnD6z/NklMHdZyy84jM/AAQVpfUfhLv0IM4O39C0LEz3WEKIcQJC1o3AmAWL81yJKOLWbYStt8a/vcJFiA6EdaEVT1TfCMoKweA1Nbv4dX8Ba/pOSJpapEjhBi9ZAR0hDN6WmME7duyHIkYC/yWcP2nUTy4BPTVlBnrTWKDzl0nHZcQQgyF1j5+a7iswCiSBHQwjFg5ZtnZqJxJaRsBPUxFinqTTwCz9HQA/KZn03odIcToJCOgI5xZMA8PXikUIMQQaaeNoGMXGDZm0eKTPp/KmRpOEU/UoL0uqXgohBh2QcfucP1nrArjVa1BxPHFln55WK5jliwHZRC0bZbfF0IIGQEd6YyCcATUb38ZrXWWoxGjmd/yIod7eyozetLnU4aFkTsdIExshRBimL3SfkXWf45kysrFKFwEOuitxC6EGL8kAR3hVKwS7EJw29DJ2myHI0Yxv+UFAMyTnH57JCN/NoCsAxVCZIXfk4DK9NuRzyw9A6C38q4QYvySBHSEU0ph9oyCBm2yDlQMjda6T//PdOlNQGUdqBBimB25/lMq4I58VukKIExAtQ6yHI0QIpskAR0FjIK5QDgNV4ih0IkadLIOrHyM/FlpO+/hBNSXEVAhxDALOveA1xX2JI5XZjsccRwqdzoqWoZ2WuShpRDjnCSgo8DhdaBSCVcM1SvTb09BKTNt5zVyp4My0F0H0H4ybecVQojjCXr7f8r029FAKfVKNdxGmYYrxHgmCegoYBbMA8JpjjpwsxyNGI385p4EtGR5Ws+rzGhYDZeAoHNvWs8thBCH+R278eqfQGv/lW09/T8NKUA0asg6UCEESAI6Kig7D5UzGQKXoHN3tsMRo4zWPn7LBiC96z8PM6UQkRAig4JELcn1V5Ha9HWS6z6D374drYPeBFRGQEcPs3gZKIugfRvaact2OEKILJEEdJToLUQk60DFIOlEDXidqGgZRrwq7ec/vKZU1vQIIYZCu+04e+4iSBxd6V1rn9SW74LfHfaR7NhBct2nSW26oed7rQIjPiELUYuhUFYco2gJoKUdixDjmCSgo4TRMw3Xl0q4YpCCrv0AGHkzMnJ+I09GQIUQQ+fs/TXunrtIPv95gu6DfV5z9/2WoG0TKlJM/MyfYU99JygDv+FJAMxiGf0cbayedaBe07NZjkQIkS2SgI4ShoyAiiE6nICGazXTz8ifGV6ncy868DJyDSHE2KQDD6/2b+F/O00k119D0HUAAL9jB+6eXwIQWfB5jHglkdkfIX76bRiFiwAwK1+flbjF0PUWImp+XupaCDFOSQI6Shh5M8CIoBOH0G5HtsMRo0jQtQ8AIzczCaiyclHxiaDd3mRXCCFOhN/0HLhtqJypGEWnoJ1mki9cg9++g9Tm74D2sCZf1NtDEsDIm05s+XfJed39fbaL0UHlTEbFq8BtJ7H2o3i1j/UpLiWEGPskAR0llGG90nOxZxRU6wB3/+9IrL+a1Pb/xWt8Bu11ZzNMMQLpw1NwM5SAwiv9QINOmYYrhDhxXu1fAbCq3kTslK9gFJ+KdlpIrvs0uvsAKmcKkVkfPuo4pRTKig93uCINlFJEF16NypmETtSQ2nIjiWf/vafKsc52eEKIYSAJ6ChyeB1o0L6NINlA8oXrcHb+hKB1I97BP5B66b/ofvxdJJ7/fG+SKsY3rX2C7nA6W0YT0LyeQkSyDlSIcS1I1JFY91m82jXH3Ve77fiNzwIG1oRVKDNGbOl/9bSLCkCZRBddgzJjGY9bDC+zcCHxM35MZP7nULEKdNc+Upu+jlf9cLZDE0IMA0lAR5HDlXC92jUknv04QeuLYBcRmf9p7OmXhutEtSZo20xq0w1o38lyxCLbdLIeAgcVLUNZuRm7Tu8IaIdUwhViPPMO/ZGgfSupbd8/bm9gr+7voD3M0tMwoqVA2Fs4uuS/sKe/n+iS/8TMn5P5oEVWKMPEnvhm4mfejj39/QB4hx7IclRCiOEgCegocngEVCcOgdeJWXo6OSv/F3viW4nM/CDxFTeT89p7ULnT0cl63IN/yHLEItsyXYDoMPOIVixaBxm9lhBiZNI6wKv7Z/iXwCG15dvoYOAHoV5Nz/TbCW/ss12ZESIzP4BVdmbGYhUjhzIi2NPfA1YeQeeu4z64EEKkl3vwAZy9/zes92+SgI4iKlaJypkCRoTI3NVEl34VFSnuu4+dR2T2vwHg7v012mnNRqhihAiGYf0ngIoUoaJl4CfR3Ycyei0hxMgUtG9DpxrCGRfxiQSde3B2/bz/fTv3EnTsACsXs+ys4Q1UjDjKiGBVvBYAr+5vWY5GiNEjSNSgva4hH+81rsXZfivu7p/h7rs3jZEdmySgo4hSKhzlPPuX2JMvRCnV735W6WmYJSvA78bZc/cwRylGEp3hCrhHMo4YBRVCjD9e3T8AMCvOJbroC6AMvAP34TevP3rf2kcBsCrORZmRYY1TjExW5SogXGYkM2mEOD6v4SkST19BYu2VBMmGQR+v3U6cbT/o/bu7+xf4zS+kM8QBSQI6yigrFxUpPO5+kdkfAQy86gd7e6qJ8We4RkABjLzD60ClEJEQ443WPn59OP3WqnwdZsE87BkfACC15btop+2VfQMfr/axcN+qNx59MjEuGUWLUNEKdKqBoHVTtsMRYkTz218mtfnbQIBONZJ88UuDbtPo7Lwd7TRhFMzHnvZeICC5+VtDSmYHSxLQMcrIm4418XzQAc6u27MdjsgCrTVB9zAmoAVzgXAURLudGb+eEGLkCFo3oZ0WVKwKIz/8LrCnvRujcBHaaSbxwjWkdvwIt+YveNV/DveNT8IoWJDlyMVIoZSBNeE8ALxamYYrxECCRA3JF78MQQqzchUqdyq6ax/JjV894QKkfvN6vJqHQdlEF3wOe+YHMIqXg9sWFjIN3Iy+B0lAx7DIzA+CGcdvXIvfvCHb4YhhplMN4CdRkWKUXZDx65klKzDy56JTDTg7/jfj1xNCjBzeEaOfh5eHKGUSXXgN2IXorn14B+7H2fo9nO23hftWvXHApSRifLIm9EzDbXhcKvkL0Q/tdpB88T/BbcMsWU50weeInXIDKlpG0LqR1JbvoLV/7HN4CVLbbgHAnvF+jNypKGUSW/QFVLScoH0bzo4fob2ujPXmtTJyVjEiqEgx9rR34+7+Bc6unxIv+e9shySGUdCz/jPTFXAPU4ZJdOHVJJ77BF7tY5hlZ/YWlRBCjF068PHqnwDC9Z9HMuKV5Jx5O37bFoLO3b1/wMCqOj8L0YqRzMidhpE3i6BzF37Ts1gV52Q7pIzSTit++zaCtm347duBACN3KkbudIy86RjxiWBEwbBBmfLAZpzTgUPypa+guw9i5M0guviLKMNCxcqJnfI1Euuvwm94AuflW4nMuXLAHsrO7p+hk3UYebOwp76zd7uKFBJd8iWSz1+Fd+iBsC2SGUNFS1HRSiIzLsUsWpyW9yIJ6BhnT7kEd//vCDp2ECRqMOJV2Q5JDBM9jOs/DzNypxCZ/RGc7beR2vYDjMKFvf39hBBjk9+yAdw2VM5kjLwZR72u7HysspVQtjIL0YnRxpqwCmfnLry6v43ZBDTo2kdy0zfRXXuPfq1loBlrCsw40QWflYe745R38AGCtk2oaFnYCeOI/u5G3gxiS75McsOX8Kofwmt4EnvShWHR0kgR2k/i1T+BV/MXgtaXQJlEFnwOZfRNBc2CeUQXXY2z+5dhL/me7ga6+xDJju3ET78VIz7hpN+LJKBjnDKjmCWn4tc/jt+0DmPyhdkOSQyTYBgr4B7JmvQ2/MZn8Jufx9n6faKnfG1UPrVN7fgJ3qE/oqw8sAtRdiEqWkJk2nsw8qZnOzwhRgy/Pqx+a1WcOyo/62JkMStfDzt/it/4HNrtQNn52Q4prbTTSvLFL6OTdWDGMPLnYhbMxyicB8oi6NqP7tobtipK1kHggvZA++B349X8RRLQNNJuO0HHToyixShjZFfk9hqeAiAy+98wYuVHvW4Wn0Js2ddxdt1B0P4y7t67cfffG+YBLRvB7w53NKJEZl/R28P91ayK12FVvC6cfut1oVONOLt+ht+0ltSmG4iddtNRP6sgUYffuhFl54dLvyLF/cbYe40h/gzEKGKWrOhNQG1JQMeN4ayAeySlFJEFnyOx9kr85nW4e3+FVfE6VKy8z3QQHThopw3ttqKMKFh5KCuvtyWD1jr8pRs44dSjAaaSZIJ78I94B34XxuG0gNPC4VUQKaeN+KnfGLZYhBjJdOD23hRZleceZ28hjs+IlmIULyNoWY9X/zj2pH/Jdkhpo/2eKZTJOoyCecRO/fbRv9sGmCkQJOpIPH0ZfttWtA5QSsq4DFWQbMBvfBqv4alwNFAH2FPfRWT2FdkObUDabSdo2wLKwixdMeB+ZvEpxE67maB1E+7+3+I3rcVvXAuAUTAfq+rNWJXn9hk9HYhSCuw8lJ1HdOFVJJ77BEHHDpwdPyY67xO9+3n1j5Pa+j3wE32Oz1318IDnlgR0HDj8D9Vv2YD2Hem5Ng5orY9IQKcN+/WNaCnR+Z8itenXpFX/AAAgAElEQVQbuHt+ibvnl+ELdiEVOkpXTTd4A1TKNSKACp/68kovOBWrwsibEf4pmINZejpKmWmP3W9ej7PjhwBEFlyFWbIsTJSdZlIbv0rQ8gJBojYtU1CEGO385vXgdaJypw/7wy4xdlkTVuG0rMfZfSfKzsMsf+2oH13XWpPaehNB+1ZUtILokusH9WBVxSpQ0TJ0qhHdfQCVhd/tY4Gz+xe4e399xJYwkfdqH8We9aGM3Fekg9f4LBBgFC07bvKolMIsXoJZvISgcy9+60bM4qUndT+o7Hyii79E8vnP4R16ALNoMWb5OTi77sA7cB8ARtESlBFFOy1op/mY55MEdBwwoqUYeTPD4g9tmzBLlmc7JJFh2mkKp1rYBWAfv29sJlgVr0PPbcWrfxKdqkcnG8Bte+VLR5m9FXp1kApbt3id4Yhn7z5WmJAGDjpZg5+swW8MR1vMylVEF16d1puSoOsAyU03hE9Dp70X+3CPwmgZMAuv/Bz8ujV4NX8lMvMDabuuEKOR1hrv4B8BsCpfn91gxJhiVbwWr/phgrZNpDZ9A7P0dCJz/x0jXoXWPkHHTvzmDehUA1bVmzF72oCNZO6eu8Lp6mYOsVO+ghEtGdTxSimMwgXhjLa2LVl5uDza+a2bwuRTGZhlZ2KWnY1VtpLEuk+jE9UELS+O2Htkv/EZAKzyMwd1nJE3PW3LhsyCOUTmXImz/VZS227GOPAHgvat4XrS2R/FmnzRCd+TSQI6TpilKwg6d+M1PTdiP1wifXoLEOVMzepTY3vyRdiTLwpj0gHaaWHfrs1Mn30K2PlHTSHSWkOQAq3BiKCM8EmkDjx090GCzj0EnbtxD/0Jv+5vuHkziEx7V1pi1W4HyZf+C7wuzPKzsWd+8Oj3M/EtPQnoI9gzLh2xT0qFGA5e7aP4zc+DlYdV9eZshyPGEGVGiS3/Dl71Qzi77sBveo7E2isxi0/Bb9vaZwaNd+gBzMrziMy6HCNWkcWoB+bV/RN3792AQXTxdf0W6zoRZuFC/PrHCdq2wsS3pjfIMU77DqltNwNgT3tfn4fIVuV5uHvvxqtdk7Z7ZO11oZ3WsILsSS4h0oETzjYBzNLsFnOzJl2A37YJv+7v4Wh+pJToki9iFi4c3HkyFJ8YYcyS03H33YPftA7mXJntcESGZWv957EoZaCipXh2FSrS/6isUgr6+aJWhoXqfYp3HkbhfFIbv4a76w6M3Klhhc2ToLUmtfmb6MQhjLxZRBdc3e/6GqNoCSpehU7U4Devxyo9/aSuK8RoFaSacHb8CIDInI8NejRHiONRysCedAFW+dmkdvwYv24NftNz4WuxKsySZWBE8Q49iF+3hkTDE9hT/hV76rtRdt5R59Pax69/kqBjB9aUizGiZcPyPrTX3dsbOzLnoyf1e8Poucn327amJbbxxN33a3T3QVTOFOzp7+nzmlX5+jABbXiSiP8JlBk9qWtpp5XEc59Cp+p7LpCPESvHyJuBPeuKQX9fHi4gZOTNwIhXnlRsJ0spRXTep0m5HWBGic77FCpSNOjzSAI6ThiFC8DMQXcfkPVr40C2KuAOF6v8NQQzPoC755ekNn8b47TvndQUk6DlhfDpol1AdOn1KCve735Khb0L3d0/x6t+WBJQMS5prXFe/gF4nZilp2NNeEO2QxJjmIoUE1v0BfzJFxJ0V2MWLe5zD2NPeXtYobP+H7j77sE98AesCauwJ1+IkTcTrQP8+sdx9t7dOzvIPfQgkZkfxJp8YcZnsrj770U7LWEBmMkXn9S5jLyZYETQ3QfQbjvKLkhTlGNb0LkHd989AETnf+aoCq5G7hSM/DkEHTt6+s8Ovcqw1j7Jzd8Kk08zJ1xW5HUQdHaES+ESNWHxKcM+4XP6TWERoWyPfh6mrDixZTec1DkkAR0nlGGFZZgbnsRvfh5j0gXZDklk0EgcAU03e/qlBF378Ov/SfKlrxCd/ymC7gMEHWGjexUt6WnSfPwveWffveE5p/zrcadwWVVvwt1zJ37jM2inBRUpTsv7EWKkCRK1uPvuwciZjDXx/N7CF37dmrCqoplDZN6nRn1xGDE6mIUL+53mZ8QnEFt8HX7bv+Ls/gVBywthH8TqhzAKF6G9TnTPQ1kVrcDIndxbbM6rfYzIvE9i5E5Fp5rRbivaacPIm5mWkaYgWY+7P6yoHpnz0ZP+rCjDxsifS9C2Cb9t60nP/hkPtPZJbbsFtI816W2YRYv63c+qPA+nYwde3ZqTSkDd3b8Me7naRcTPuA0VKUY7rehkLalN3yBo24Kz40d9qsgeO36N3xCu/zTLzxpyXCONJKDjiFm6IkxAm57DlgR0zAor4Pb8sh3DRQqUUkQXfI5kopqgYyfJDdf13aEDvLp/vFJIaAB+xw6ClhfAjGNPettxr2tESzFLz8BvfAav9jHsqe88mbchxIijAx/v4O9xdt8ZrskGnD13YU08H6viXFLbD08nvPKYfd6EGE5m4Xzip36ToGsf7sEH8GofJWjbDISJpz39vVhVb0IZNl7D0zjb/4egYwfJdZ866lwqWkb8rDtOui+ks+tnEDiYFecOeo3cQMzChQRtm8J1oJKAHpd38E8E7dtQ0TIisy4fcD+z8lzY+ZOT6j/rNT6Du+83gEFs8XUY0VIAVLQEoiVEl/wnyfVX4R16ACN/DvbE8497Tt21B52qD/tq5s8ZdEwjlSSg44hZckQ7lsAZ8Q13xYnRTht+y4uoeFU44un3tDixclGRsb0uS5kxokuuJ7Xxq4AOn1rnzUQ7rbj7foN34H6sCW845lNnd99vAbAmvvWEf+FYE9+C3/gMbvXDWFPecczz68DvLaYkhNYar/avmPlz01aZ8DDD78BveSmcCdC1H51qwMifg1W2EpU744RGX/yOXTjbbibo2AGAWf4atNtB0PoS3oH78Q7cH24vOU0KD4kRycidRnTeaiKzLserfzycAVbx2j73PFb5WZjFy3D23BVWclbhVF8VKUYn69GpRrzav2FPfMuQ4/DbX8avWwOGfczEZ7CMwgXh+du2pO2cY5EOHNy9v+mdehuZu/qY7UvC/rOnELRswGt4ctD/74NEDaktNwJgz7ocs/iUo/YxC+YRmfsJnG3fx3n5Voy86ZgF8455Xu/w6GfpyjHV+1US0HHEiJWjcqeju/YStG7GLDk12yGJNEhtvQm/6dmevxnhkzayXwF3uBixcuKn/3efbTpw8GoeIejc1VNWfVm/xwbd1fj1j4Mysaf86wlf0yw5HRUpCSvztm3GLFr8yrV9B791I37zOvymdejug0QXX4dV8bqhvUExpgStG3G2fi9sxXDqtzELTu6JdpBqwq/7O17to0zo3EOyuu/rfsNTuLt/gYpWYJadgT35ogGn5nu1a0htvRF0gIqWE5n3id4pfn7HDtz99/e0kYgTmf/pcfH9IkYvZeUcc4RJWXGic/6NyKwPgzJ6/z17tY+R2nIj7v7fYlW9eUg3/Vrr3iJd9pR/TWvdDbMnAQ3aX0YHHsqQW/lX81s3kdp2C7r7AAD21HdhncD0VavyPJyWDXh1fx9UAqr9FKmNXw+r6JeddcyZUfbE8wk6tuMdepDUxq8RO+VrqNxpA/47613/OcZGu+Vf7ThjlZ6O27UXr2mdJKBjQJCoDasCKrunOutBdKoRAOM4T9XGMmVEsCa9DXfPL3EP3DdgAuoeuA8IsCrfOKiphMowsarejLvvN6S23YIRq0D7CbTXjU7U9E5bPMzZfRdm+Tlj6umlGJre6pV+N8kN/0F8+Y19RkK11ng1f8FvWotV8XrM8tccNYKu/SR+w9N4tY/1lOYPAAhUFCt/OkbOlPCGJlJM0LoRv+lZdKoe79ADePX/JH7G//ZODTssSDWT2n4b6ABr0tuIzPowysrpfd3Mn4O56Br0nCsBPaSqh0KMRK/+fJkV56J2/QLdfRC/8Wms8tcM+pxhq5QtYBdhT3vP8Q8YBBUpQsUnhn0rO/ec9EOssUQHPs6O/8U79AAAKmcy0fmf6fOQ+Fis8tfgvHwrQcuLBKnGE66U7Gy/jaBzFypeRXTB54/7cC4y52NhW7m2LSSe/TiYsZ4ZXLPCtc6lK1B2PkGqiaD9ZTAiY+6eXRLQccYsXYG7/1785ueAf8t2OOIkedUPARqz4rXEFl2D9h2C7gPoZD1m8dJsh5dV9qQLcPf9H37TswRdBzByp/R5XTuteDV/CfcdQi9Rq+rNuPvvQXcfwO95ynqYkTcTs3QFZslppLbciO7ej9/8vFTNFb1TW1WkBO00k9xwHbHl38XImUTQfYjUth8QtL4IhKOXKlqONflC7IlvIejci1f7KF79E+FUewBlYZadiTXhjexpKWbO3AV9L1j1RrQOCDp24Oy8PRyB3XYL0aVf6XOT5Oz4396qtpG5qwe8gRqohZIQY4UyLOypl+Ds+CHuvnsxy84e1PF++w5S2/8HgMjMy4457XOozMKFeIlqgvatkoAewat5JEw+lYk97d3Y096HMk98uZmy8zDLzgjrpdT9A2PqO457jFv9cHgvYUSILv7PflsAHXUdwya6+Es4O35E0LYZnWokaNtC0LYF79CfQJlh2zc7/L41i0896V6iI03GEtDbb7+dH/zgB9TV1TF//ny++c1vcvbZx/8QP/3007ztbW9j7ty5PP3005kKb9wyCheCGUd37Zd2LGmg3XaCzr0EXXvDNVfJenTgQOCBdgEDa9IFx12HOKRrBy5u9SMAvUWllBnBzJ8F+bPSeq3RSEWKsCa8Aa/6IdwD9xOd37fQhHvwD2FxiLKVGEMo1mTkTCS2/HvoZB1YOSgzjrJyUJGSPqND1uSLcXf9FHf//ZKACoKO7QBEl34FZ9dPCVo2kHzh2p4HGveGJfvtQuyJb8VreALdfRB31x24u+7ocx6jYD7WhDdgVZ77SiuG1h39XlMpA7NgHtGF15B49uP4Tc/i1TyM3dPI3mt8JpyKbkSPmXwKMV5YE9+Cs/dXBO3bCFo3Av235no1r2kdqU1fBz+JWbIca2Jm1kkbhQug9lH8ti3Yky/KyDVGI6/2UQAi8z6NPcSfvVV5Hn7Dk7gH/4hZed4xe3b6HTtxtt/Wc81PYubPPOHrGNESYovD4onaaSPo3IXfsRO/6XmCto1hJd0eZtmZQ3ovI1lGEtD77ruPa6+9lptuuokzzzyT22+/nXe9610888wzTJkyZcDjWltb+djHPsa5555LTU1NJkIb95RhY5aejl//T7zqh4nM+tAJH6u1T9C+Hb/5efymdQTdB7HKzsKe9q4x3e6jP9p3SL705T5fEANx2rfiNzxJdP6n+rTsCKfRPYX2E1gV557QU7Mj+Q1Pg9uKyp3e25xa9GVP+dewHH/to+GT6J7RmyDZgHvwT+E+U9895PObhfOhcP6xY5j4Ftw9dxG0rCfo3IORN2PI1xOjW1iKvx6MKEb+TGJLrif54hcJ2rbg7r0bAGvCG4nM/jdUpBB75gfxm9fjHbgfv/l5VLQCa8IqrAlvOGpE/0QYsXKic1eT2vJtnB0/xixehrILcV6+FQhHa+ShpBBhgTt70oW4e+8OHwzlfPC4x7jVj+C8fAvoALNyFdEFn81Yj9HDFXUDKUTUK+iuDn8eRvSk2qiYZWdg5M0k6NxN8oVriS//Tr9LDrTbEa77DFysiW/FrnrTkK+pIoWYJcsxS5bDtHej3Y7wQWHD0xCksCrHXg2JjCSgt912G5deeimXXXYZADfeeCOPPfYYd9xxB9dff/2Ax33iE5/gfe97H1pr/vjHP2YiNAHYky/Cr/8nbvWfsae/D2VGj7m/1jr8Ej7w+7C66hG82r+GFR3LzsKe9u7exfFjnVfzcJh8GhGMvBkYudMwcqej4lXhz1PZYFgEnXtwdt6O3/g03Ws3E527GhUtxav5C1794+AnAHB23o5VdT72lLef8A2gW/1nAOxJ/yIjFgMwcqeGD1yansM99AD2lLf3NCr/PQQpjMJFA/YESxdl52NNPB/v4B/DkdgFn8vo9cTI5XfsBMDInx3emFpxYku/SnLjV9BOK5E5H8MqPa13f6UMrNIVWKUr0F4CzOhJryM2K1+P2fgUfv3jpLbchJE3A51qDKvlTrn4pM4txFhiT74Id/9v8Zuew7LeAPQ/1VUHblhttechkj3t3dgzL8/o72WVOxXMHHSyflBrFccyr+5vAFgV56CsExux7o8yIsSWfYPEC19Ad+0j8cK1xE/9Vp8kVOuA1JbvopO1GPlziMz5+EnH3ycGOz+c4TLhDWk970iS9gTUcRw2bNjAJz/5yT7bV61axdq1awc87vbbb6e+vp6rr76a73znO+kOSxzBKFyEkT+HoGNH2Mdw0r8MuK/Wumf6YNiqQsWrMEtWYJauwIhV4h76U1gwo/Fp/Mansae/j8jMy4brrWSFDpzest7RhddgVZwz4L5m4QLM0hWktt5M0LKe1OZv9nndKFgAZjQs+33w93gH/4jZcwOqnVa004L2usJRkbkf632aGnQd6EmAo2P6Cyod7CnvCBPQA/eH027ddgDM8nOIzP3Y8MQw+e14B/+EV7uGyKzL+4yEi/EjaA+n3xoFc3u3KTuP+PIbj3vsydxQ9TmPUkTnfZJE66aeXoKbQBlE5mdutEaI0UhFCnsfHuZ1PAq8vs/r2k/iVT+Mu/+3PcX/DCJzP449+cLMx6ZMzML5+M3rCdq2YpzgiJ/WGp2oRkVLx9SawrC91WMAabknUpEi4qd+i8T6L6C79pLccB3RU24IC1M1PYvXuDassGvlEV38xUGtMxWhtCegTU1N+L5PeXnfipLl5eXU19f3e8zmzZv59re/zV//+ldM88R/Ae7Y0f96l3TJ9PmzKW6fTTE76Np1Dw1ds2GAJ3X5bQ+S3/4wGoOW0g+TzOnpa9QC4ILxFowJZ5Pf/jC5nY/TVf0k+/zBLdgfbXI6H6co1YhrV1HdWg5tJ/DvJPdD5DCHgtbfo40Y3TlnkMg9A88ORzutyEHyOtYQ734+rGr7Kt6hP9HeUkNryf8DZVLQch95QFd8OdV7qo/af6Qb1s+WzqHcnoTtHgIgFZ1Fe+HFuNEZsL+Fnn/MGVccX0I88RJ1L91JR+HAD33E2FXcuIE40NCVTyJDn4ET/WxFC95DaeMPAejIW0V1rQ+1Y/d3nhBDYfrLqeABcrrX0f6P9+LaE/CsKrSyyOl6CjPoAsC1qmgvuphUYj4M0++3PK+SAqBp71O0tx1j5pTW2M4+4okNxLpfwPKbScSW0FL+0WGJ84Rpjek34ZulA96TDsRO7aY8UYNvFrK7MRea0vP/wCi6klLnB9ide+h+8v0odO9rgZFDS/FlpA52AB1pud5YM2fOwAWyMlaE6NVTD7TW/U5HSKVSXHHFFXzta19j+vTpg7rGsd7YydqxY0dGz59tOphB4ukHsVO1zChtxypdcdQ+zt7f4LY/DBjEFl/HlGM8YQsSk0g8/ThRIznGf24Oiae/ggby5n2YoorBtDqZi/bfD4ZFwVHT6OYA5xGkGvGbN6Cs3J6m2EXoRA3JjV8hp3sd+Xm5ROd/hu6adQCULngvFaOsAl42Plt+5dU9Pd3eSE7pSkqyMGXZL/sAyReuJj/xFJWnfuy4U9/F2NNdX40GJs557ZDWcB7P4D5bc3D2Jgk691C54BNMGEOjIUKkzxyc6Htw9v0W02/F9FuBbb2vGgXzsae9h5yylRQNc5str+kcUi8+RF73UxSwF+xClF2IMqNoPwFed9gaLFmPdpr6HBtPbqZkaukxC+wMt9T2/8Gr+WPP+tnPH9Ue55jHvvwwHhCb9EbmzE5vC7pgxvdIvvAF6D6IypmCWXoGVtkZGIWLyJcerEOW9p9caWkppmkeNdrZ2Nh41KgoQG1tLdu2bWP16tWsXr0agCAI0FpTWlrKvffey6pVq9Id5rinDAtr0oW4u3+Gd+C+oxJQd/99uLt/DiiiC6867oLuw3PjtdM24MOGscCr+Ss61YjKnY45hN5gx5umYUTLMKre2HdjfAKxZd8gueFL+PX/ING5C7wOjPzZGPlz+z+R6MMsnI+55EtZjcEoWtw79d3ZfhsqUox229FuO0budCIzP5DV+ERmBanmcJqemYPKmZTtcACITH9vtkMQYsSLzLyMfd6ZzJqcT9C1j6BrH9ppxip/DUbR0qzd75hFi1CxinAdaOeeY+6romWY5edgVZyDu+9e/Ka1+A1PYIyQCrpe/T/xDoa1X/y6v5HyE0QXXXdCU1t14ODV/QNIz/TbVzOipcRPvxXtdgyqX7g4trQnoJFIhGXLlrFmzRre/va3925fs2YNF1109D/0iRMn8tRTT/XZ9tOf/pQ1a9Zw1113MXXq+KquOpzsSf+Cu/dX4RqCzr0YedPRfgpnxw97+ktCZP5nsCYc/wGAMmNgRCFIgZ+ENK1XGknCQgP/B0Bk+qUnXQxkMMzChWES+uIX0d0HAbAmXjBmE/2xSCmFPeUSUlu+3dt/9DC/4UmsqjdJBdIx7HD/z7AA0fCOlAghTpIyMHImYuRMhPKzsh0NEN53xc/8GdppRrttaKcV3Da076CsHLByw9ZgVj4qZ1Lv945O1uM3rcWr++eIaOESJGpJbbsFAGvShXh1a/Abnyb50peJLbn+uOvf/abnwOsMC0LmnXgblMFQZmxMrZkdCTIydrx69WquvPJKTjvtNFauXMkdd9xBbW0tl19+OQBXXnklAD/60Y+wbZuFC/u2kCgrKyMajR61XaSXsvOxqt6Ed+gB3AO/x576DpKbbkB37QXDJjLvk9hVJ95HSUUKw6kebmvaCmaMJOHoZz0qdyrmMQoPZYpZOJ/Ysm+S3PAfoCysytcPewzi5JiVr8NO1KDddpRdgLILcA/9Cd21D52oBklAx6zDCag0jRdCpIsyTFSsHAYxMmeWnQmGTdC2OesVdHXgkdr8LfC6MMvOJjL337En/QvJDf8R9kjecB2ReatRRhSUBYYd/u48YgmLV5O+4kNi+GQkAb3kkktobm7mxhtvpK6ujgULFnDPPff0jmYePHgwE5cVQ2BPvhjv0AN4dY/h1f8d/CQqZxLRRV8cVENdAGUX9aw1aIV4VWYCHkbad9BeB7gdaK8Td99vAIhMf3/WRjDMgrnknHUH6GBMJvljnVImkRmX9tkWdGzH69pHkKhBapCOXUH74RFQmTYvhMgeZeWE7ckansKvfwJjytuPub92Wknt+BFmyWnYr14iNAg6cACFMuzebe7unxO0b0NFy3v6pipU3gxiy28iueFagvZtJJ/r21UDI4JZugKr/ByMwoX4Tc8CBmbleUOOTQy/jK2e/chHPsJHPvKRfl978MEHj3nsddddx3XXXZeJsMSrGLnhgurwA+xiVp5HdN4nw+kbg9S7DtRtS3OUw8/ZczfunruBoM92lZOd0c8+MdgFWb2+SC/V87BGJ0ZfNWNxYrTWBB09LVjyZQRUCJFdVsW5+A1P4dX9A/s4Caiz+xf4dWvw69YQdO4hMvvDg27ZFCTqSKz7FHgdqFgVRu6UsCf6oQdBGUQXXYuy83v3N3ImElt+E8722wgStaA9CDzQHjrVGCbPDa8s3zNLlmNESwf3QxBZJeWbBJFZHyYVOFiVr8eqOn/I6wpfKUTUms7whp3X+Czunl8CKuzXaOWhrDxUpAB72nukV55IK6MnAQ26a7IcyfgTpJrQybqweJrbinbaMYsWYRYtTut1tNOEdlrC75IxMDtECDG6mWUrwYgStG8lSNZjxCr63S/orsareQQwQCm8A79DJw4SXXjtCc/C0lqT2nYz9AxO6MQh/MSh3tftGR/ELFp01HFGrJzY0v86OqaeBNSrf5ygdROgsSa+9YRiESOHJKACI2868VO/ddLnUXbmE1CtA4K2LRh5M1BWbtrPH6SaSG29CQB71uVEpr077dcQ4kgqPhGAQEZAh5Xfto3k85+FI/q6Abgooou+kNY11q9Mv50jhcOEEFmnzBhm2Rn49Y/j1z+OMfUd/e7n7LkLdIBV9WasCW8gufFr+I1rSa7/PNEl12PEK497La/6IYKWF8AuIH76reB1EnQdIOjaD2YMe+olg4rdiJZhTL4Ie/JFPdXFGzAL0tt6RWSeJKAibVSkEMjsFFx33z1hexgzhlV5HtakCzDzZx/zmKBzL37rRoz8WRj58wbsLaV1QGrLd8Ftwyg+FXvqOzPwDoTo6/AIqE7WjukWRiON37QW0KhYBUbudJRdiA4c/Pp/kNpyI5g5WGVnpOVah6ffSgEiIcRIYVWci1//eDgNt58ENOjci1+3BpSFPf1SjPgE4ituIfnilwk6d5N4+nKMgnmYJcsxS0/r9/4qSNTh7PwJANG5q3tGWivSVq3WiJbACOplKk6cJKAifeyeBDRDI6Da68Ld/9vwL34Sr/ohvOqHMArmY1W8FqNwAUbebJQZQWsfv/FZ3IN/IGjZ8MpJrDzM4mWYJaeFX5hHTDtx9/+u5yldIdGFV0mrBDEslJ3//9m77zCpyuuB4997p+7MbK90adIEKQoIIiooNuxYYozGxBZTzE+TYEwsSTTFFKPGrjGmmNhBRFFRQWkivfcO23d2d/rMve/vj9ldWLaw7M4Wds/neXwemZ3yzsJ77z33Pe85YPVAzIeKlKHJybRNGOWbALAPuA1r1b5upRRRZzbRvW8SXv8btJGPJiQd98gVUCGE6AgsmaeDxYlZuRUzeKjmZmi1yK5/EU9vvaCmRZju6kHSaY8T3vw4RvHSeApvxSaiu/8NthTsfa7B2uPSquswFW+vYgSxZJ+JJeesdviWoqOSAFQkTGvvAY3ufy/e6yn1FByDf0j0wFxi+Z9gVmwmUrG5ahBWdE8/VLQCFcqPP2ZxYsk4DdO3K773oOhLjKIv40939cKSMQbd3Tu+sgo4htwjm9lFm9KTumNWbo0XIi/6/VYAACAASURBVJIAtNUpZWBWbAFATx1S87imadj6fwcV8xM7+AGhNQ/gHP17LC0IHJVSGJUSgAohOhbN4sCSNR6j4HNihV/U2nJkVG6LXyfpdmwnXV/7dbZknMN/iYoFMLxrMUpXYpSsQAUPENn+ItF9s7H1+xaYYcyylWBLwTHoLsnuEbVIACoSpjoApRVScFUsSHTf2wDY+34D3d0bx8l3YO9/M0bRIgzveozyTSj/npp0N82Zh63npVi7nY9m8wDxhsdG6QqMkhUYZatRgX3EAvtqPsfa64qEpd0J0VRaUjeougud6AI4oi7l3wNGMJ5+e9TNJk3TsA/6PirmxyhcSGjlT9HdvdHsmWiODDRbKpghVNSHivlQUV+8SbkzG82Zi+7MRkvqHt+nrttQocL4MdGWguY89n4pIYRoK9acyfEA9NAnWNKGx/ep61aiO1+N/7zH9AZvyGtWF9as8VizxsdvtJV+TWT7Syj/biKb/ljzPMfJ34sXdBTiCBKAioRpzRXQ6IE5EK1ATxmCnj7q8GdanFjzptQ0IFYxf1W6m0JPH1GnYq2elIfe42JsPS5GmTHMis3xgLR0FZo9DXv/byd87EIci57UDQNQQamE2xaq02/1lCH1/lzTLDiG/oSwGalKM9ty/B+i29GTB9S0TbJIASIhRAdjyRgDVg8qsDdelM3iRE8eiOldB5Yk7H1mNOl9NE3Dmnk6lozRxPLnE935KipcjCV7Ipacya38LcSJSAJQkTCa7XARIqXMhO2hVEaoZu+nre8NjV7EaVY3loyRTXpfTbdiSTslvuLU76aEjFWI5tBcUgm3LZlVAagltf4AFEDTbTiGPxgvDhUuQUVKUeHSeJE1S1K8NZMtGc3qRhlBVKgIM1SIChVi+nejAvsxyzfWvJ+k3wohOhrNYsc54mFi+Z9geNfFj1vedQDYel1+OLOtqe+nWbB1Oz++supdhyV9hNx4E/WSAFQkjKbbaoqpEPPDEU2FWyJ2YG68Mm3yyfG7dUJ0MnpVKxZZAW0bRkXVCmjq0Eafp2laPD26Gb07VbQSo2ILZvkmVLgIa8/pzRqrEEK0pnjv43gfTjNciuldj4qUYO1xcbPfU7M4sGaelqghik5IAlCRUJotNb4vKuKNV/dsIWWEie59Azj26qcQJyqtKsAxJQBtdSpagQocAN2RsFYA9dFsyfELMLkIE0KcIHRHBnquVKsVrU/6TIiEqukFmqB9oLGDH6IiZeie/lgypTiQ6Jw0ewboDohWoKK+9h5Op1az/7Oq2IYQQggh2pYEoCKhagoRRRMUgBZ8DoDtpGtl9VN0WjWpnsgqaGtryv5PIYQQQrQeCUBFQmm26kq4iWnFUl2U5Vh7tYQ40VU3AZd9oK3LqOoZrEsAKoQQQrQLCUBFQiVyBVTFgvH+ebotnqIoRCemJUkl3NamTKOmpYqsgAohhBDtQwJQkVCJ7AWqQvnx93TmJqylixAd1eEVUAlAW4vp3w1GEM2ZJ43RhRBCiHYiV/UioQ6n4LY8ADWD8QBUb0YLBCFONLIHtPVV7/+U9FshhBCi/UgAKhKqpgputOV7QA+vgOa1+L2E6Oh0l/QCbW1mhRQgEkIIIdqbBKAioTRb4tqwVK8E6UkSgIrOT3PkgGZBhYtRRri9h9MpGbICKoQQQrQ7CUBFQh0uQpSAFdCqFFxNAlDRBWi6Bc2ZAxxe/ReJoyLe+P5a3YHu7tfewxFCCCG6LAlARWLZkgEdohUo02jRW5k1KbiyB1R0DXp1JdyAFCJKtJr2Kykno+mWdh6NEEII0XVJACoSStMsYEsBWrYKqpSqWQHVk3ITMjYhOjpNeoG2GrN8IyD7P4UQQoj2JgGoSLjqNFxa0AtURUrBjIAtBc3qTtDIhOjYdKmE2yqUGSF2aD4AlvSR7TwaIYQQomuztvcAROej2dNQ/pYVIlKhAgB0qYAruhAtqboSbudPwVVKgYqCGQVlgtVdp9+vilZilK7CKF0BKOwD70SzJh33Z8XyP0NFStDcJ6Gnj0rQNxBCCCFEc0gAKhLucCXcFqTgVq0ASQEi0ZV0hRXQyM5Xie59C8yjKv1qNjRnFpojB92ZhRnYj1mxFVA1T1HhUhwjHkLTm37qUsokuvcNAOx9ZqBpWiK+hhBCCCGaSQJQkXCJ6AVq1uz/lABUdB01e0BDBSjT6HTFcqIH3ie6+z+HH9CsoNsADYwAKngIFTyEecTP9dRhWNJHEN0/G6P0ayJbnsQ++O4mB5JG8RJUYD+aMwdLzuREfyUhhBBCHCcJQEXCabaqViwtScENSgVc0fVoFgeaIyveCzRcWBOQdgZG2VoiW58GwD7k/7DmTa2VcquMECpUhBkqRIWL0OzpWNJG1KTcWjLGEFr1M2KH5qE5c7D3veGYn6mUIrrndQBsva46rpVTIYQQQrQOKUIkEq6mF2gLAtDqFixSAVd0NZ2xEq4ZzCe0/hFQBtZeV2Hrdn6d/Z6axYnu7oU1cwy27hdgzRpXa7+nJXUwjmEzAZ3orn8SPfjRsT/XuxazYgvYUrF2n5boryWEEEKIZpAAVCRcTQDakiq4NXtAO88KkBBNUbMPNLC/nUeSGCoWJLzuYYiWY8kYg33ALc1+L2v2GdhP/h4AkS2PE1r/W6IHP8AMHooXNTpKdE9876et56VoFmezP1cIIYQQiSP5SCLhWroCqswIKlwCmo7myE7k0ITo8HT3SQCYvt3tOo7mUMrEKFoU38MdrUBFyzErd2D6dqG5euAYdl+8V3AL2HpegoqUEN39GkbhAozCBQDxPZ7pI7Gkn4qefioqUo5R+jXoDmw9pyfi6wkhhBAiASQAFQnX0iq4KlQIKDRHjuzZEl2O7jkJANO/u13H0RyxA+8T2fq3uj+wunEOfwjN5knI59j73YQ191yMstUYZWswytagQoXEDn1E7FBVaq4lnr5r7XERmi0lIZ8rhBBCiJaTq3uRcC1Nwa2ugCvpt6Ir0j19gfgKqFLqhGkboqKVRHa+CoC12/loSd3RbClothT01KHojoyEfp7u7oXu7oWt53SUMjF9OzHL1sSDUu96MIKg27H1ujKhnyuEEEKIlpEAVCSexQWaDYwgygijWRzH9fLqCri6U1qwiK5Hs6eDLQ2iXlSoEO0EKcQV2fUviFWip43APvjHbRo4a5qOJXkAluQB2HpfhTJjmJXb0KxudKek8QshhBAdiRQhEgmnaVqLeoGqUHUBIglARdd0OA13V/sOpIlM/15iB94DdOwD72j3VVtNt2JJHYLu7t2u4xBCCCFEXRKAilbRkkJE1Sm4ugSgoos6Mg33RBDZ/gIoE2v3aViS+7X3cIQQQgjRgUkAKlqFZmt+AKpkD6jo4g5Xwu34K6CxkuUYJcvB4sLe76b2Ho4QQgghOjgJQEWraG4hIqUUZlUPUN15Yux9EyLRalZAO3gKrjJjRLY9D4C97w01814IIYQQoiESgIrW0dxWLDEfGIF4C4Wq9xCiq4nvXdRQgf0oM9Lew2lQ7MAcVGAfWlJ3rD0vbe/hCCGEEOIEIAGoaBU1KyHHuQJas/qZlNfuhUyEaC+axYmW1B2Uienf397DqZeKlMcr3wL2Abei6bZ2HpEQQgghTgQSgIpWUVMF9xgroGa4FKVUzZ9VqGr/p7RgEV3c4UJEO9t5JPWL7PonxHzo6aOwZI1v7+EIIYQQ4gQhAahoFccqQqSUSWT7ywQXfYPw2gdQRjzN0KwpQCQBqOjaqluxKP/udh1HfUzfbmIH5gI6joG3S7aCEEIIIZpMAlDRKhorQqSMMOENvyW693UAjJLlhNc9jDIiqJoUXKmAK7q2w5Vwd7frOI6mlCK87XnAxNrjoppAWQghhBCiKSQAFa2ioT6gKuIltGomRuEX8bYNg34AtlSM0hWE1z2E6d8Xf72k4IouTvfE+2m2ZysWZRp1HjNKlmGWrQSrB3vfG9thVEIIIYQ4kVnbewCic9JqquCWEd7yFOgONIudWMHnqOAhNEc2zlN/he7piyV1GMFVMzFKV9a8XpcUXNHFaUl5oDtQkRJUtBLNltwqn6PMCCpSjop4UeFiTP9uTN8uTN9OVOAgmqsb1m7TsOZNQbOlENn2AgD2vt+s2esthBBCCNFUEoCKVqFZHGiOLFS4mNiBObV+picPwDHiYXRHZvzPnpNIGvU7gqtm1lTN1aQHqOjiNE1Hd/fBrNyK6duFJX1Ek1+rTAOjZBmaLQXdfRKazRN/XClUYD9GyVfEir/C9O2Itz5q7L0CB4jueJnozlfQ3X1QwQNorp5Ye1zSou8nhBBCiK5JAlDRapwjf4tRvgHMCMoIgxlBs7qwdrsAzZpU67m65ySSRv+e0Or70ZK6oVkc7TRqIToO3XNSPAD17z6uADSy7VliB96r+bPmyIoHs8FDqODB2k/WdDRbGpo9Dc2ejubuje7pi+7ph+7qiVG2htiheRjFy2rSge0DbkPT5fQhhBBCiOMnVxCi1ejuXujuXsfx/D4knfEKaLI1WQho3j7QWMGCePCp2dA9fTD9e1HhYoxwcfwJ1mQsmadjzRqLJf1UsKWiNTLnrFnjsGaNQ0XKiBV8DroDa9bYlnwtIYQQQnRhEoCKDkVWVYQ47HAl3KYFoKZ/H+HNjwNgH3gbtp7TUcpABQ9h+vei2VLRUwejaZbjHotmT8fW64rjfp0QQgghxJHkal8IITqo6hYnpn8PSpmNrlQqI0Ro/SNgBLHkTK7Zo6lpFjRXT3RXz7YYshBCCCFEoyTXUQghOqjqfZkYQVSooNHnRrY+jfLvRnP1wDH4R2ia1kajFEIIIYRoOlkBFUKIDkxz90VFyjB9u9GTumEGCzBKv0YF81FGEIwQKlqOUbIcdDvOU36BZnW197CFEEIIIeolAagQQnRguuckzLKVRPf8j8jOV1D+PQ0+137y99E9fdtwdEIIIYQQx0cCUCGE6MCqA0qzYnP8AYsLS8Yo9OSB8ZVOixPN4kJ39ZDgUwghhBAdngSgQgjRgVlzJmF616HZUrBkno6eOhRNt7X3sIQQQgghmkUCUCGE6MA0ixPHkP9r72EIIYQQQiSEVMEVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmJAAVQgghhBBCCNEmWi0AffHFFxkxYgS5ublMnjyZxYsXN/jc2bNnc8UVV9C/f3969uzJlClTmDt3bmsNTQghhBBCCCFEO2iVAPTtt99m5syZ3HPPPSxcuJCxY8cyY8YM9u3bV+/zFy1axFlnncXrr7/OwoULOe+88/jmN7/ZaNAqhBBCCCGEEOLEonm9XpXoN50yZQrDhg3jiSeeqHls9OjRXHbZZTz44INNeo9zzz2XM844g0ceeSTRw2uSbdu2MXDgwHb5bCE6M5lbQrQOmVtCtA6ZW0IkVsJXQCORCKtXr+bcc8+t9fi5557LsmXLmvw+Pp+PtLS0RA9PCCGEEEIIIUQ7sSb6DUtKSjAMg+zs7FqPZ2dnU1hY2KT3eOGFFzh48CDXXntto8/btm1bs8fZFK39/kJ0VTK3hGgdMreEaB0yt4Q4Po1lDSQ8AK2maVqtPyul6jxWn1mzZvHAAw/w0ksv0bt370af25rpEJJuIUTrkLklROuQuSVE65C5JURiJTwFNzMzE4vFUme1s7i4uM6q6NFmzZrFHXfcwbPPPstFF12U6KEJIYQQQgghhGhHCQ9A7XY7I0eO5LPPPqv1+Geffca4ceMafN0777zD7bffztNPP81ll12W6GEJIYQQQgghhGhnrZKCe9ddd3H77bczZswYxo0bx8svv0x+fj7f/va3Abj99tsBeO655wB46623uP322/n1r3/NhAkTKCgoAOLBbHp6emsMUQghhBBCCCFEG2uVAPTKK6+ktLSUxx57jIKCAoYMGcLrr79es6dz//79tZ7/8ssvE4vFuO+++7jvvvtqHp84cSLvv/9+awxRCCGEEEIIIUQba5U+oJ2BbDgXonXI3BKidcjcEqJ1yNwSIrESvgdUCCGEEEIIIYSojwSgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCCHahASgQgghhBBCCAGsLYlw0G+09zA6NQlAhRBCCCGEEF3equIIZ79XxHlziqiImO09nE5LAlAhhBBCCCFEl6aU4oHl5ZgKDgQMfrWior2H1GlJACqEEEIIIYTo0uYfCPNFfoQUm4ZVg5c2+1laEG7vYXVKEoAKIYQQQgghuizDVDz4dTkAPzk1mbtHJKOAHy3yEjZU+w6uE5IAVAghhBBCCNFlvbEzyIayGD3dFm4d4uHeEckMTLWypTzGn9dWtvfwOh0JQIUQQgghhBBdUiim+M3K+H7Pn49KxmnVcFo1Hp+QBsCf11ayqSzankPsdCQAFUIIIYQQQnRJL272sd9vMDTdyrX9XTWPT8xz8O1BLqIm/HBRGTFTUnETRQJQIYQQQgghRJfjDZv8qSrF9uHTUrHoWq2fP3RaKt1cOsuLojxQtUdUtJwEoEIIIYQQQogu5w9rKigLK87MszO1h6POz1PtOi9NzsCmw9Mb/Ly61d8Oo+x8rO09ACGEEEIIIYRoS+tLozy30Y+uwSNjU9E0rd7nTchz8Kcz0vjhIi/3LPEyIMXKhLy6weqR3tkVYHlRhF5uK708Fnp7LPRNsZJsa3jtryJiomvgaeQ5nYUEoEIIIYQQQoguw1SKe5d4MRTcNsTNqZn2Rp//rZPdbCqL8sxGPzd+Wsqn07Ppk1w3jFJK8cjKSv5YT+VchwV+OzaNWwa76/xs4aEwN35aQtSEa/ol8d0hHk7JsDX/C3ZwnT/EFkIIIYQQQogqr20PsLQwQk6Szv2jU5r0ml+fnsqUHg5KwibXf1JCfsCo9XNTKWYuK+ePayuxaPCDUzx8d7Cb83s6GJRqJWzA/y3x8vOvvBhHFDT6344AV31UTHlEEYgpXtka4MxZhVw0t4gP9gYT+r07ClkBFUIIIYQQnVbUVCwrjPDJ/hCHAgYz+rmY0sPRYMql6Ny8YZMHv463Xfn16amk2pu2HmfVNV6anMF57xex0RtjxBv5XNXPxfeGeRiaZuVHi738a1sAuw4vnZ3B9D5JtV7/r21+frzYy9Mb/OyqMHhxcjrPbPTXtID53jA3Nw508/IWP69tC7C4IMLiglLeOj+TKT2cif0ltDPN6/VKTeF6bNu2jYEDB7b3MITodGRuCdE6ZG4JEVceMdlYFmVDaZQv8sN8diBMRbT25e6gVCt3DvNwbX8XSdbGA1GZW53LPUu8vLTZz8Q8O3MuyDruGxF7fTF+vqyc9/eGqP5X1cdjYY/PIMmi8e8pGZzbQMD4RVWqrTeiyHLqFIdMNODRsancOcxT87zKqMmvV1Tw/CY/Z+Ta+eCi7GZ+245JVkCFEEIIIcQJ7aDf4BfLy1leFGGfz6jz80GpVqb2dJJm1/j7Fj9bymPcvdjLr1ZU8MfxqVzZz1XPu4rOZlVxhJc3+7Fq8Mfxac1aBe/tsfKvKZnsqojx7EYf/9oWYI/PIMWm8b/zMjkjt+ECRZO6Ofj4kmyu+biEXZUGTgu8MLnuammyTeeXY1J4fUeAJQURFuWHmXiMwkcnEglAhRBCCCHECWtbeZQr5pWw3x8PPJ0WGJxmY1iGjdFZNqb2cNYqGHP3iGTe3RXk6Y0+VhVH+c6CMiqiipsH1S0OIzqHsKF4bqOPx9ZUooA7h3kYkt6yIj99U6z8fnwa941KYfaeIONy7AxKO/Z7Dky18ckl2Ty/yc+FvZyMzKq/AFKyTeeOoR5+t7qSP6+tlABUCCGEEEKIYzFMxScHwvR0WxjWClU9VxZFmPFxCSVhk9OzbTwxMZ2BqVasesMrWzZdY0Z/F1f3S+LxdT4eXlHB3Yu9VEZMfjA8OeFjFO1HKcUH+0L84qtydlbGb1Bc2MvJzJGJ+3tOc+h86+Tju3mR6bRw36hjFz+6faiHp9b7mH8gzKriCKMaCFZPNBKACiGEEEKIJtlYFmVlcYSwoQgb8ZUlu0VjSo94pc/qlEalFPMPhHnw63I2lMVItmksvzKXPJclYWP57ECIb35aij+mmNrDwT/OycB9HD0UNU3jxyOSSbZp3Lu0nF9+XUF5VHH/qOQmpWYapuIfWwP8YXUFwzJs/GFcGv1T5dK6IyiPmMzeHeQ/2+MprAAnp1p5dGwqU3ueOAV90h06twx288R6H39eW8k/z82s+dmmsijf+7KMHKfOT0emMCb7+IPTVcUR7lniJRBT/Pr0VM5ro9+NzBIhhBBCCHFM+QGD8+YU4Y/VrV95PzAw1colvZ2Mybbz3EYfX+THL/x1DSqjige+Luf5szJaPA6lFK9uDXDvUm9N38S/TUrH1siqZ2O+O8SDx6Zz15dl/HFNJYGYySOnpzYahC7OD/PTZeWsL40CkH8gzIRZBfzk1BR+eIoHu0Uq7LY1pRQf7Q/z721+5u0PEa7aCpxq17hvVArfGexu9r+R9vS9YR6e2+TjvT0hNnujDE6z8cHeILcuKMNXNRfn7S9iWi8n941MbjCl90iBmMlvV1Xytw0+qjvCzPi4hIt6O3l0bConVaWsK6XYURFjW3mMsTl2Mp0N30CKmqrJv18JQIUQQgghxDH9fnUF/phiWLqVsTl2HBYNp0WjIGjy4b4g28pj/GWdr+b5aXaNe0Ykc14vJ5NnF/L6jiA3ndyyYiqFQYMfLvLy4b4QAHcOdfPI2FT0FrZUuW6AC7dN4zufl/L0Bj/dXBZ+cErdNM3ikMHMZeW8uTPen7Gn28Ivx6Tw+cEwr20P8JuVFbyxI8ATE9MY10gxGpF4T6738UBVexUNODPPzjX9XVzaJ4k0R9NXxjuaPJeFGwe6eXGznz+vrWRYuo2Hvq5AAVf2TaK3x8Lzm/zM2xdi3r4Ql/R28sCYFE5uYD/qgoNh7l5cxq5KA12Du4Z5yEvS+f3qSubuDTH/QIjr+7s44Df4ujhCWTgeoabZNX59eirfHOiqdXNmwcEwv1xezrrSKANTrYzOsjE6y85tQz31fj5IG5YGScltIVqHzC0hWofMLdGatpdHGfdOIQpYcnlOnWIrMVOxuCDCe3uCLC+MMLmbgx+PSK658P/dqgp+t7qSoWlWFlyW0+hKyUG/wfe/LMOmw/hcB2fk2hmVZWfevhA/XuylJGySatf44/g0ZvRPbPXat3cGuGVBGQD/OCeDy05Kqplbm8qiXPtJCXt98eqlPxqezI+Ge3BZ499x4aEwP15cxo4KA5sOn07PYXgr7HsVdS04GOKKj0owFdw3KplvDnTTw524dO/2tqcyxui3CjCOiNruH5XMvafG08WLggZ/Xefjxc0+QgZYNLjpZDc/G5lMrstCxFDM2h3k+U0+lhfFV+2Hplt5amI6o6tSd/MDBg98Xc7rO4K1Pjs3SScnycK6qtX+iXl2Hp+QhlLwwNcVNTeDjub9do8Gv48EoA2QE7kQrUPmlhCtQ+aWaE03f1bKu7uD3DjQxZNnph/360Mxxfh3C9hdafCb01P4fj2rixAPPqd/WMSOitqtVOw6RMz4/5/d3cHfzkxvtQDj8bWVPLSiAocFZk/LIqNiL/tcvbj5s1IqoorRWTb+fnZGrcq61UIxxY8Wl/G/HUGGZ9j4dHr2CZn2eSLZ54tx9uwiSsIm945I5hdjjl3c50R0x8JS/rsjiMuq8eykdC49KanOc/IDBr9bVcGr2wKYCtxWjcv7JvHJ/hAFwfgESrVr/OCU5AZTxZcWhPnsYJjBaVZOy7bTs2qevbkzyM+/KqcoZGLXwVDx/zzW+F7q7wx2s7MixsriCCuLozw9qeHjhASgDZATuRCtQ+aWEK1D5pZoLSuLIpw7pwinBVZcldfswG/evhDXflKCx6qx/Kpcuh1VkOhQwOCSD+LB54gMG98b5uGrwghLCsJs8sZwWuDh01K5dYi7xSm3jVFK8X9LvPx9S4AMh87VuSFe2mfHUHDZSU6emZRes+pZH1/UZOK7hezxGcwcmczMJlQ7Fc0Tiiku+qCIlcVRpvRw8PrUTCydNOAvDRk8vdHPFSclHbOi9BZvlIe+ruCDI1Ynh6ZZuW2ohxn9ko6rWNeRysImD35dzqtbA+gafGugi/tGpZB7nMXFJABtQGMn8pipOBgwSLPrpNhP3JxyIVpCKUV5RB33vgq5SBaidcjcEq1BKcWlHxbzRX6EH53i4eHTU1v0ft+YX8LcvSEu7ePkT2ekkZ0Uv3A9FDCY/kEx2ytiDM+wMfuCLNKPOL+UheOrLs29cD5eMVPxjfklfLQ/XPPYPSM83D86pUnB7xeHwkz/sBirBp9Oz2ZEZudon9FaFhwM88jKCq7pn8TNg9yNttE50o8WlfGPrQF6eSwsmJ5NRiNFcrqiRfnx1czJ3RycmWdvUnXnplhXGiXJAgNSm5di3iUC0PyAgdumkXwcB60jT+SlIYO/rPOxsSzKrooYe30GMQUuq8Ytg9x8/xRPQsuKC9HRbfZG+fFiL0sLIjwzKZ3rBjR9D45cJAvROmRuidYw/0CIqz4qIdWusebqvBYXc9lTGWPcquTbkgAAIABJREFUOwWEqjJsc5N0hqXb2FUZY1elwfAMG7OmZXaIQMIXNbnsw2LWlkR4fGI6Nww8vl6PP1ni5YXNfk7JsPHZEam4hUGDuXtD7KmMcShgkB80KQgYDM+08dj4NFK72OJGSchg/DuFFIXiKaLD0q38fnwaZzZQrEopxcriKK9s8fPPbQEcFph3UXaTqr+KjqFTB6CmUty7pJyXt/gByHbq9E220jfFws2D3JzRSHWy6hP5Zm+U6z4pYXdl7b0IOUk6hVW51A4LfOtkN3cN89DHY0nY3QUhOppgTPGnNZX8dX0l0aq9OCl2jaWX59K9iSlZcpEsROuQuSUSzVSKybOLWFca5eHTUvjR8Pr3bR6vuXuDPL42fmPfd0RLl1MybMzuIMFntZipWLtlO6OHHP/cOjIV954RHoal2/jvjgDzD4RrFZM50tB0K2+cl9WpCugcS/X+4hEZNrwRk72++DX3FSclcXnfJGw62HUNmw4riqP8d3uAreWxmtf/7cy04745INrXCR2APri8nOknJTEmy1Yn6FNK8dNl5bywyY9Nj/egCh8RQzotMPuCLMbm1B+Ebtu2jR3Onty6oIzKqOLUTBs/G5lMvxQrfTxWkqwaq4sj/GltJe/tOZxf7bBAbpKFbi4LfTwWfjoyudnL04myrTyKXdfq3SwvRFN9mR/mB1/Gy3YD3DLIzX5/jI/2h5nW08F/p2Y26eaLXCQL0TpkbolEe3dXkJs/L6W7S2fFVXkkWRN7g91Uir0+g/WlUQ74Da7p76qVdttRtGRuVafiHsmqwdSeTsZk2chzxa8Zk6waP17sZWt5jG4unf9NzayVtpsfMFhVHOGsbo42S0NOJKVUvdcI1VWHPVaNLy/PITfJwpPrK/nLWh/BhqJ04otKM/oncf0At1QaPgGd0AFo2t8PADA4zcoDY1K4sJcTTdNQSvHA1xU8ud6HXYf/Ts3k7O4ODgVMdlXGeHWrn9d3BEl3aHx0cTYDjwoQlVI88PluntptRxG/A/O3SWkNbjjfWBblL2srmbc/REWk9q9zQIqVhZdl1/va9/cEeWtXEKXiAbKuQYpd565hHvqlJCZYLAkZjHijAIsGn1+ak7D3FV3LR/tCfPPTEiJmfBP7XybE+5sdChiMf6eA8ojiubPSubYJ5fDlIlmI1tFR5tZeX4weLkunLQTSVZhKMWlWIRvKYvzpjFS+M7jhnn6dXUvn1i++KuepDT5GZ9m4rr+LK/slkVXPKm9Z2OSG+SUsLojgsWo8Oi6VvT6Dj/eHWFMSb4ExKc/O29OyTpjKumFD8fJmP39ZV0l3l4VHx6YyoSq1tiBgMP7dAsrCiscnpHHzoMOrmPt8MZ5Y7yM/YBAxIWoooqYi12VhRj8X5/ZwnDC/A1HXCR2A/mypl9l7ghwKxHMBx+fYeei0FOYfCPPYmkqsGvzz3Awu7F27THHMVNzwaSnz9oXo7bHw0cXZNXs4VxdHeGhFBZ8fjG86P7LHTlP4oyYFQZNDAYN7lnjZ7I1x2xA3fxifVut5n+wPcc0n8X5FR0t3aPzr3MwWNWqu9uxGHzOXlQMwPMPGxxdn40zwHUzRuR0ZfN46xM2jY1NrHfT/vc3PXV96SbNrLLsi95iV0DrKRXIiFAQMHBbthG5wLTqPjjC3Ptgb5Pr5pVzVN4kXJ6fLlpQT2Ny9Qb4xv5RuLp1VV+V16WuHls6t4ynaFzYUd31Zxps7a/diTLLEU1Aroqre68r2Uh4xeWaDj1UlUU7NtDEx187pOXYcusYbO4M8uqqiJqW22tX9knj4tFT+b4mXeftCTOnh4M3zmpZFJTqHEzoAhcN3Vh5bU0lp2Kx53KLBy2fHGwjXxx81ufTDYlYURxmeYePJiWn8dZ2Pd3bHJ7zbonjmrMx6e+w01eriCFPnFBFTMGtaJpO7O4F4SuyUOUVURBTfHezmjNz4Squp4K2dAebtD2PT4YmJ6Vx/HMVd6nPWrELWlkZxWTUCMcUtg9z8eULHOGiJju/j/SFumB8PPm8f4uZ341LrTXe/+uMS5h8Ic0lvJ/88N6PRk0hHuEhOhHWlUaa9X4QO3HNqMncO9XTpCzTR/tp7bqmq/YJrq5qV/3VCGjcNkn1ZR/OGTe5fXs4p6TZuHdL0ap9tSSnFuXOKWFUc5bdjU7lzWNdd/YS2n1umUvx+dSVz9gQ5M8/B+b2cTMh1sLYkwvQPi4mY8MTENL518vHNr8qoye9WVTIy08aMJmQsQfxa9ntflNHLY+GSPklc1NtJptOCP2rywiY/j6+rxHtU9p9Vi9dKOVi1QDQkzcrPR6ewoTTK4+sqCRmH+7qm2DWWXJ7bpfa8ik4QgFariJg8ud7H3zb4CMYUz5+VfszJVRwyOH9OETuPKDDksMCtgz1c5ink9KEtP9g8trqCR1ZV0sNlYdHlOWgaTJ1TxLbyGJf0dvLquRm1ynkbpuIXy8t5ZmO8cNK9I5L5+ejkZvW7WlcaZdKsQtLsGv+bmllz0HpxcjpX92v4d1MeMbnrizKynDozR6VIhd8uojRk4I8pTAUKWFMS5baFpYSN+MrnH+oJPqvt88WY8G4hlVF1zH9f7X2RnAj+qMnZ78XncbU+Hgu/Pj2V6X2cchdXtIv2nlvV1VKTLBpBQ5Fk0fjs0mwGp8n+rCP9/CsvT2+In+NHZNh4YmJah6veWf13me3UWTMjt9Gel11Be8+tI/1zq58fLPJi0+G9C7IY30hBzSOFDcW1n5TUZPjdONDFY+PTGr1xuqM8xrS5RRSHDi/w6BqckWtnW3msphjnhFw7Nwx0saEsyqL8COtKo5gKerot3Dcqmev6u2pS8vf6YvxyeTmzdsfrpzwzqeWLLeLE02kC0GolIQNvWNE/tWl7HXdVHJ5c3xjgYubIZHp6rAk72MRMxbT3i1hRHOWa/kmUhUw+PhBmaJqVjy7JxtPARvIXN/n42bJyDEWzVy2rT3LfHezmj2ek8eImH/cuLcdjjV8UHL33FeJ33a6fH09PBvBYNX4yMpk7hnpwWOSiujPaUxk/Gcw+opjWkb472M1j4xsOPqv9fbOfHy/x4rZqzLs4m1MaKArQkU7kzfX9L8v417YAg9OsPDgmhV+tqGCTNx6MnpZt4+xuTkZl2RiTbZcbOKLNtPfcuviDIhblR3hoTApbymO8tj3A0DQr86fnJLx4zYlqry/GaW8VEDGhh8vCgYCBrsUzTO4fndLgNUFbUkpx4dxilhZGElr59kTW3nPraD9b6uW5TX6ynTrvX5hFnsuCoypFt74FC8NUfGdBGe/uDpLh0AnETEIGnJpp49VzMuotUnkoYDDt/SL2+gym9HAwvU8S7+0JsuBgmOrCxaOzbPxydApnd3fUukYoj5jsKI8xNN3WYIC7pCBMYdDkUrlp2yV1ugC0OcrCJsGYqtVGIpEHm23lUc6aVVRTzSvDofPp9GxOOkZV2vkH4umPIQP+cU7D6cT1iZqKIf/Lpzhk8ukl2YzOtqNU/AD09q4gw9KtzLkwu061uUdXVfCH1ZWk2TXG5diZV9WAuV+yhftGpXB6jp3eHkuzVmRFxxKImTy+zscTVekwDgtkVxVF0LV4GvtV/VzcP6ppe6CVUty+sIzXdwbp6bbw6fRscpLqBl8d7UR+vN7aGeA7C8pwWmD+JTkMy7ARMxV/3+Ln0VUVlIVrH1J7ui18/xQP3x3cMVPtROfRnnPrq8Iw579fTIpdY/2MPHQNzp5dxPaKWM1NUAF3LCzlvzuCzOiXxF8mpPHbVZU8s9GHqaCXx8LzZ6U32iKuLVRXbU13aKydkXdcPdQ7q4523oqZiqs+KmHBoXCdn+Ul6Xx3SPyck+bQUUpx79JyXtrsJ8Wm8d6FWWjAjZ+WssdnkO7QeHxCOtN6OmuCRW/Y5KIPithYFmNMlo1ZF2TV3Bzxhk0+Oxgiza7XCTyFaCoJQBuQ6IPN8xt9/HRZORYN3pmWxVndmnaCeWGTj58sLSfVrrHoshx6epq2sltdCGJwmpUll+fUHCAqIibnvFfIjgqDnm4LL0w+fLKbsyfINz8tRdfgrfMyOaeHk/kHQvx8WTlbjkg19Fg1BqdbGZ5h45bBHil/fQJacDDEXV962e+Pp5/P6JfEQ6eltngPRiimuOTDIr4uijI2287sC7Lq3P3saCfy47G7MsZZswqpiKp6q0KWR0wWHgqzsijCyuIoq4ojVETjh9gRGTb+PCGN07I7Vqqd6Dzac25d90kJH+4Lcc8ID78ckwrAmpII580pImLGCwJO79P8mgrNoVR8S0FTq/GGYor1ZVF6uONtMRJtQ2mUM2cVYtVh+ZW5NTehVxdH+OEiL2tLo+ga3DMimZ+OTG63Cp+XfljMwkNhfj4qmZ+OTGmXMXQ0HfG8VRoyuGVBGWtLokQMRcRURA5nyuK2atw0yIVF03hyvQ+HBd46P4szqwpcesMmty8srVloSLJonJFr5+zuDj7YF2JJQYSBqVY+vCiLzA7Ul1V0DhKANiDRBxtTxVdI+qdYObuqGFFTKKW47pMS5u0Pc2aenVnTsmqdTHeUx1hSGOaqvq5aKU43flrCe3tC/Oq0FH54VPrMXl+MWz4v5eui+MnuvpHJXNwnifPnFOGLqTopN1FT8ffNfubuC7GpLEpB0Kz1flf2TeLno9q/36lomsKgwelvx1unjMiw8fvxqQm9414QMJgyp4j9foNr+iXx3Fm1K2F2xBN5fT7YG2TevhAum0a6XSfNofPa9gAri6NNKrYE8Xk/d2+ImcvK2e830ICbB7k4p7uTgqBBfsAgP2hyksdyXNW2hahPe82tjWVRJrxbiNMC62bkkX1E5sMzG3zc91U5GQ6dlVfltlnF6H2+GNd9UoJS8MHF2aTa636uUoqP94dZcCjMV4VhVpdEiZrxrIUVV+UmfNvJtR8XM29/uN4KphFD8dtVFTy+zocinsr/5MR0FLC9PMbOihiHAgbn9XQypUfTVp2qA+ohadYm941cVhBm2txiUmzx1U+p8B13opy3lFIsPBTm8XU+Pjt4eHVU1+DVczK45KibQKZSPL3Bx2vbA2woi9X6WXeXzryLs+nVxIUPIY6HBKAN6EgHm6KgwYR3CykKmTXBYUXE5I9r4qk7UTN+svr3uZnkuiyUhAwG/y8fQ8HGa/Lq3YMWNRWPrIyf7OBwNbIr+ybx0jFK55eEDDaWxZi7N8jLW/yEjXi65vUDXDw4JqXWxYfoeG5bUMrrO4NM6eHg9amZrdKrb11plAveL8IfU9w51M13B3vol2JB07QONbfqs98X46fLypm7t/49sT3dFr64LOe4mqX7oyaPrankqfW+mr0zR3t3WuZx3ZzqzHxRE7uuYZd95w3a7I3isWq1smLaa25VH1NuHeLmsaMCK6UUF39QzOKCCD86xcPDp6e2+nj2VMaY/mFxTeuHm0528deJ6XWeV10ksJoGOKsKKDWnwmhjFueHueiDYjxWjVVX5zZ4nvziUJg7vyiryU6pz/gcO/ePTmFSA5lUoZjiH1vj1UkPBUxS7RrfOtnNdwe7693rd6RrPylh3lEr2aJjXRM21ZqSCE+s8zH/QIhHx6byjYGN/3suChosPBTm84Nh9voMfj8+VQqIiVYjAWgDOtrB5uP9IWZ8XIJVg5mjUnhhk4+CoIkGpDt0SsMmPd0WXpuayeL8MD9bVs75PR28fl5Wo+87/0CI2xeWURwyGZZu5aOLs5t8pxTiF+uPrankX9sCGAqm9nDw5vmNf6ZoPwsOhrhsXglOCyy9IveY+5BbYu7eIDfML6X6ANPTbWFydwfdDS/OtCyKQwbFIZPSsIlN1/DYNNxWDbdNw23Vj/h/jQynzsAUG32SLa22jzJmKp7b5OfRlRX4Y4pkm8Zdwzy4rBreiIk3rAjETO4c5uHUzOal0W72RnlsdSWBmCLPpZObZGF7RYw3dwZl7gA7K2L8dV0lr20PMDC1/n3qrSViKB5aUU6yTWfmyNZdjf70QIh+Kdbjnn+lIYM3dgb597ZATXutv52ZxhV94xUk2+O8tbsyxpi3CtCAlVfn0rue1ZKVRRHOnVOEwxJPPa3vOYmyqyIefO73GwzPsLHFGyViwqxpWUzufjhgW5Qf3+doKrh7uIdJ3Ryclm1n3r4Qty0s4+RUK0uvyElIvQOlFNPeL+arogg/G5nMfaMaT2v1hk1+utTL+3tD5Ll0+qdY6ZdixWXVeGVLoKbl3ORuDq7tn0SKXSfZppNs01heFKkJPAGynTpFVRVMdQ0u6uXk/tEpDEmvG1hsKI0ycVYhSRaNddfkkiVplzU62jWhECc6CUAb0BEPNj9d6uX5Tf6aP5+ebeP349Lo5bFww/xSviqK4LZqpDt09vsNXjk7g8v7HnvPTX7A4O1dQa7sm9Tsip1bvVHOeLcQgB3Xd5O0nQ4oFFNMnFXAjgqDX45O4Z5TW7+y4Uf7Qvxne4CFh8K1+vQ2l02H/ilWhqbbuPfUZIbWcxHVHKZSXPZhMV/kRwC4tI+T341Lq1WYrLWUhgyGvV5A0FAsuTyn3gvDzm5NSYTH1/qYtSeIecQZaVyOnXemZbZ6C4ioqfj2Z6XMqVr1/s3pKXz/lNaZH9V77d1WjaeOCB4bUxoy+MnSct7bE6zZ41Xd6gTgB6d4eHBMCrt2bG/T81ZJyOCmz0r5Mj/Cdf2TePasjAaf+53PS3lrV5Br+ifxfCPPa4lt5VEu/bCYQwGTcTl23jgvk+c2+nhkVSV9PBYWX56D26ZTGjI4c1YhBwMmPx7u4cHTDq/0RU3FqDcL2O83eG1KBhf2Pv59q4ap2FkZY6s3xrbyGGtKoryzO0iWU2fV1bktKupTETF5dqOPp9b7avaX12d4ho2fjUzmot5OVhVHeW6Tj3d2BYmakJuks/zKXFKOSku+bWEpr+8I1psi3NV1xGtCIU5kEoA2oCMebIKx+EXyfn+MX4xO4boBrpq7s6GY4oeL4hVIAdLsGpuv7dZof6dEu+SDIr7Mj/Dy5HSubKQPpGgfv1tVwe9WVzIo1coXl+W0aXqjqRTrS6MsOBjm632l9M1JI8upk51kIcOhEzUV/qjCH1P4oib+WO0/FwZNtpXHaqWlpdg1/jMls6agQku8uyvIzZ+XkuXUeXJiWrMuOlvi3iVeXtzs55sDXTx1Zt1Uwc7s2Y0+Zi4rB+I3GK7t7+La/q6aNMRpvZz8+9yMVl35vm1hvDq4x6rhiyksGrw7LavBFMfmUkoxdU68LVe16uCxoe8XNRVXzCvmy/wIugbndndww0AXF/ZK4h9b/dz/VTkxFV8N+3mvMtJ7nMSqkngBrK3eGKl2nW5une4uC91d8SyEphYUUUpxKGCS6dTr7IdcURThps9K2e83yHTofHxJNv1SGl7Z3F0ZY+zb8fYjn0/PTnjfy/yAweTZhRQETSbk2vnfeZkk2+LHlnPeK2J9aZQ7h7p5dGwq11W1Ghubbef9i7LqFPv52wYf939VzoRcO3Mvym7yGIpDBv/YEuClzT4OBurecPvrhDRuGpSYtN6ysMmLm3xsK49REY0fJyuj8cyNO4d6uKh33dYWBQGDb8wvYUVx/Hfx23GHg8w9lTFGv1UAwKoGVrK7so54TSjEiUwC0AZ01IONqRQa1JseppTiz2t9PLKqgh+e4uGh09p2/8aT6yv55fKKVr3DLZpnR3mMM96NX/y9f2EWExMQtDVXS+aWP2qyvSLGn9ZUMntPCLsOL0w+vhZFRzOVYtKsQjaUxfjzGWncMjhx+76aamdFPI3RpseLuOR2kd6hb+wIcOvCMiDeB/GHw5NrKjFv8Ua5YG4RZWHFDQNdPDUxLeFpsaZS3PlFGf/bESTZpjFrWhaz9wR5fJ2PbKfOgktzEroKXt3eIsOhc/dwDw+vqMBQMCnPzt/Pyag35bH65kReks4HF2XT96ggb1F+mJs/K6UoZKKhiJ8hGpaTpPPutKx6sweUUqwsjrKkIMyywgjLCiMUBk2SbRrTejmZ3icpvnd8R5CZy7xEzHgmzivnZDapgvYvvirnqQ0+zurmYNa0zIT+fc5c5uXZjX7OyLXz5nmZtbaSrC6OMGVOEaaCbwx08e9tAVLtGl9cllNvoFUZNRn2ej4VEcX8S7IZc4zK1etLozy9wcdbuwKEq+6RdXPpDE23MTDVysmpNkZm2hjdASpgrymJcM57RWjAgktzavo1/2Splxc2+bm2fxLPyfm7jo56TSjEicoyc+bMh9p7EB1RaWkpmZmZ7T2MOjRNa/CkrWkaE/Ic3DHUw7Sebd/YN8Oh88ImPwcDBj8Y5unUvUK3l0e55INi/rrex8ayKMGYIidJb/VUweZQSnHLgjJ2VBh8Y4CLO4d5jv2iVtSSuWW3aOS5LFzaJ4mysMnyoiizqhprH+sisSFz94Z4dpOf7i6dv01Kb5denekOnXWlUTZ7YzgtGmd1b98+gG1h/oEQN39Wign86rQUfjEmtVZKYJbTwsRcB2/uDLKyOIo3bDIkzVonbbC5TKW4e7GX/2wP4rZqvHl+JqfnODgzz8GywggbvTG+KgxzXX9Xg4W6dlfGeGWLnwN+g8Fp1mMec+9Z4mVnpcGPhnu459QUzsxz8MmBEJu8MV7fEaCXx8qg1MPv8/fNfn67urKmfcKwelpe9fZYubqfi6+LIuz3m3R36ZzVzcG1/V3cMdTNBb2cnJZtZ1CqlZiCnRUGb+8KcHY3R60tFwf8Bjd+WsqvVlbw6cEwW8tjNXuhK6OKjWUx3t0d5Mn1Pj7YF8JQcOsQNy9NzmjyPt3RWXZe2eJnS3mMMVl2+qcmZpWtKGhwx0IvMQWvTc2s064sz2UhFFMsKYywrjS++vzCWRmMzal/njksGuURk6WFEcojZqNp0l8cCnPh3CLWlEYxFUzr6eCx8Wk8Nj6N6wa4mdrTyagsO93aIJ2/KfJcFopDJl8XRdnkjXLDABfFIZM7vigjpuI39KSQYF0d9ZpQiBOVrIA2QO52HT+lFGPeKmBnpcGHF2Uxvp2babeWpQVhrp9fQlm47tQ5I9fOK2dndKgVrK+LIkydU0SaXWPFVbnt3s8rUXNLKcVf1vn41YoKIL6C9tBpqbXaETXlPc5+r4g1JVF+Ny6VO4a2X3C+tCDMBXPjzd/Xz8g7rmJgJ5oVRREu/bAYf0zx/WEefjO24WyNj/aFuH5+CVXbHTkp2cLEPAfjc+x0d1tIt+ukO+L/pdobvkF3tFe3+vnhIi9OC7xxXu102+KQwdmz462Ebhzo4nvDPOS5LKTZNWIKPtwX4u+b/Xx6RJuD07NtPDY+rcHU0nWlUSbNKsRl1Vg/I5eMqnl40G/w7c9LWVYY3398Xg8Hj52RxgG/wWUfFhNT8MykdK4fcOxtDas3bWPkkIbnViimuOnzePppik3j9fMyGZ/r4M2dAe5Z4qU8oshw6Fzc28m4XDvjc+z0T7Gyu9Jgzp4g7+0J8VVRBJdV4/EJaVzT//i3Wjy1vpJfLK9gcJqVLy/LScgNn1+tKOfPa31M6+ngfw0U3gvFFJNmF7KtPMatg908dkbjexwPBQxGvBGvJr/iytw6K88Qb2k1aVY87XdGvyTuG5XSaBpyR+ENm5z+dgFFIZOnz0xjZ6XBH9dUckEvJ/+dKkFWfeSaUIjEkgC0AXKwaZ77lnl5ZqO/TmGHzuLdXUFu/6KUsAHTejm5d0Qyi/LDfH4ozJKCMGEDJuTamXVB3X1F7eXuRWW8sjVwzAv9tpLoufWfbfFAIqagf4qFp85Mb3Jf04/2hbjmkxJyknTWXJ13XMFroimlOO/9Ir4uivLY+FRuHdK+K9WtZas3ygVziykNm1zXP4mnJ6UfM1vik/0hnt/kY2lBpNHCK32TLUzvk8SlJyUxJsvWYDAaiJmMeauAQwGT585K59p6AqmVRREumFtUq7G7wwIOXasZg8MCF/dOYlF+uKYq+bcHufnlmJQ6q4K3LijljZ1Bbh/i5vdHFXgxTMUrW/08vKKCiojCaalehVPcNczDI02ct02ZW1FTcduCMt7ZHcRl1ZjUzcG8ffHiS9N6OXlyYho5jayAFQQMNI1Gn9OYsKEY+3YBe3xGQv6de8MmI97IpyKq+OjirAZXNSG+Yj3/QIhvDnQ3qcfn974o4z/bA/UGrIapuOrjEj4/GGZCrp3ZF2S1S/ZEc722PcCdX5SR5Yzvky2PKOZdlMW4TnrjuKXkmlCIxJIU3AZIukXz2HT4744gFRGT73SiC+iysMlzG33cvcSLoeA7g908MymdXh4r43MdXDfAxY0D3by5M8Ambwxf1GRqz/bv6eiPmtz1ZXyv1hNnpnWIsvqJnlvDM+1M7eHkq8IIW8sN/rMtQFk4XoiksUJLqmr/38GAycyRyUxMcMGZ46VpGik2nXd3B9letUrT2dLYFxwMc/XHxZSFFdN6Onjx7KYVF+qXYmVGfxc/OMXDhb2dDEi1ku7QyXVZSLXHC+TETCgMmSwrjPDq1gD/2hrAFzOZmGuvE4g+sc7H+3tDjMy08YfxqfUGqt3cFkZk2ikMmtgtGlFTEYhB2ISBqVbuPTWZ587K4LoBLm462U3EhBXFEVYWR/nX1gC93JaatNw9lTHuXuxF1+ClszNIPSqNWNc0RmfZ+cYAF4VBgzWlMcIGTOnh4G9nHjtAr9aUuWXRNKb3cbLfb7CyOMqOihhuq8Yfx6fx69NT8Bxj5d1j01u0Om/VNXp6LLyzK8hXhRFuPNnVoq0LT23w8fGBMJPy7PxkZOPtTdIcOqOz7E0OFPulWHlps59NZTEGpVk5+Yj06Or2Y1lOnXcvyKrzd9rRnfL/7N13eFRl9sDx7y1TUgiEEHrvvfdeFLuoq2Lbgq4/da1r722tKzZWXVEsa68oRRSQIlKlS0kE6TUJCQlpU275/TFJIJKEkExmJsn5PA/PAzN33jkD3Mk9933fc+J1lhwKLLX2moHVO/f+yRYnAAAgAElEQVSdoj1MbSbXhEIEl8yAlkLudlWMz7Rp9+khsv02Gy9tdMqm15Hq9yw/U5NyST7q57csg9T849MgT/SP47busSVetK5K8XL+D0fwWzBtVDyXnqIacLbfIsdv06SKluwW3uUekOhg/vkNq+Q9TldVnVte0+aFjdm8/Gs2pg3t43Tmn196H8nFBz1cNDed+i6VXy9rdMoL71AwrMAy9j05Jq8Nr8c1p2gcXl3Yts1bSbk8+EsWpg3jm7t4f0z9oO6ZNi2blak+Zu7OZ/YeDwfyAtVgHuxTh3tPSEyOeEz6fJVCtt8+qTfkqeT4LbJ8Nk2j1RLP/6Sjfu5emcmygnY+57d08+KQekz+NZu3k3LLXaBtySEvyw57+Ue32NNKbE7n3LJsm2fXZ5N01M+TA+qGdOmobdv8aV46Cw96+XOHaP5zisrPu7MN5u7zoCpwdYfjCWuu36LHlylkeC1mnJXAqKbBv+k3aVEG3+wOVJcf1NDJE/3j8Jpw0dwjAEwfn8CYZuG/2VgRWzL8jJyZimnDF2ckML5F9fwcoSDXhEIElySgpZAvm4r766J0Zuz2VNtlhPtzDMbNTiPlhKQzWlfoVE/njh51Tllx9e2kHO5ZmUW0rjD/vMQSC4dAYDZo0uIM/JbNsotKrsZYWefOSWN5io8pw+rxl46RkcxU9bm1Md3H//10lN+yDM5r6eajsfVLTBYK/25C1RO1vD7Znss/lmYSrSssuiCRTvWqd19Qr2lz94pMPtyeB8CdPWN5qE9cqYV9gsGybWbszufaxUexgQ/G1OfCgvP2vpWZTE3K5cxmLr4cX/J+wcqwbZv/bcvjkdVZZPtt4l0KHgPyTZtlExqW+n0QDNXp59bvWYHe0X4Lfjw/kf5/KCK2Md3HjN35/LDXw9ZMo+jxlrEakwfXY3wLd1G7lP6JDuafl1glhfd8ps3/tuXy/IZsjngCPxMKe7De06sOD/Wt3rOGX+7IY1+uyT97lHxTVQRUp3NLiOpAluCWQpZbVFy+YfPdXg+2TYWKVJRlc4af25Zl8mu6HxtoFK2WuddyS4afx9YcK+oz2C+x9H1hEJiRvHheOruyTYY2cvLS0Ho80i+Ox/vHMalTLJ3LkQz0beBgT7bB+nQ/iw56OL+lu1jlTtu2eX1LDjf+fJQ8w8ZnBfZ7jQ7y3fsdWQaPrDlGtK7w2vD4cu15CoWqPrcaR2uMb+7mk9/z2JxhkFBChdz3knOZlpxLXafCtFH1I+bvBqB7fQe7jhlsSPez/LCXKztER8x+4lPJ9Fr8a90x3k7K5d3kXN7cmsvkjdksT/ERpSlMHRnPTd3qVPnSYkVR6BLvCCTxB73M3e9hfAs3+YbNP5Yexbbhf2MTKryP8VTv3buBk8vaRrEty2DrUQOjYNb35u5Ve6OjOv3cqu/WyDcCs9a/pvv5c4dAX+s8w+KhX7K4dVkmK1J8pHkCbWDObRmFpsDvx0y+3JnP1qN+vt2dT47f5sUh9ehQRTdqNFWhX6KTv3WKQVcVNqT7yTdtRjR28tppLI+OVN3qOxjSyCXJ5ylUp3NLiOpAZkBLIXe7Ki4t36TjZ4dxqLDzqiZBW9q4P8fgzO/SOHRCg2+nCgMbOunbIFCtsU2cTts6GtuzDP6zOadYlUoI7HN5Y3h8iRUNTcvmqgXpzN3vpX2czo/nJ1KvnO0F/ijfsBn/XRqbMvwowKimgbYIZzZ38eCqLL7YGVjSdWnbKL7amU+8S2Hr5U2CWgTnX2uzePHXHK5qH80bI8pe4hZKoTq3ZuzO56+LMnCqgRmWngmBJPTVTdk8tiZQOXfy4Lr8PQJn6XP8FmNmpbE9y+DqDtG8fsISxSMekze35OLWFW7rHlvmPtdQsmybK35MZ95+70nPtYjV+HBM/VIrxFYV27a5saDPZ/MYjW7xOnP3e7myfTT/DcE5Yds2H/+ex8zd+Tw1oC4dq3g2u7r93Mr1WwycnsqBPJOXh9SjZ4KDG5Yc5fdjBroCf+0Uw/kt3Qxr7MKpKRiWzZtbc3h2fTa5RuDSpVt8oJpuqBKow3km8/Z7mNA6qtrt+xQVV93OLSEinSSgpZAvm8o5c3Yqq9P8fDy2Pue1KnvJankc81mcPSeNrUcNhjRyMqihk8UHvWwsmAktTbSucHWHaPo2cPLYmixS8y2idYUn+sdx3R+KvBRW8I13KSw4v2Gl90QdyDV5YFUmP+zzFKukCRCjK7wxIp4LW7kZMyuNDen+oO75MyybHl8e5lCexZxzGjC0ceRUNgzluXXn8kze/S2X9nE6iy5M5KWN2by8KQeI3OSz0JYMP+Nmp+Ix4Y3h9Ti/VRSvb8nh9c055BRcfPdOcDBtVDzt6x5PbAzL5tPf8/hmVz5d4x1c2T66Spd9Fnpu/TGe25BNvEvhlaHx1Hep1HEo1HWqNI/VwjaL6zFsLvghjdVpgf6PLg3WXNKIFlWw5D3cquPPrW925TFp8VFidAWPaWPa0Lmezpsj4ku9YbE/x+CBX7KYv9/DR2MTIqLgm6jZquO5JUQkkwS0FPJlUzmTN2bz1Lpj/KVjNFOGVW6mwW/ZTJwfKFjRoa7O/POOz0we9Vr8fMjLb5mBao67sk12HDNwawqTOsVwbeeYoiI0GR6Te1dl8VXB7GO0rtA6VqN1nE6MrvDlznwcKnx7VgOGBTFhO+q1+HZXPp/vyGNlqo82dTQ+HpdA1/hAUlC4569nfQc/XRicfUyF7UXaxWmsuaRRRC2vCuW5lW/YjJuVytZMg5axGntzTDQF3hhRcuuNSFPYqzJaV3BrChnewJ2Mcc1cbM8y2JtjEq0rPD+oLld3iGb6rnyeXX+MHcfMYuP0rB9IRK9sH13hWf2yzNvnYeKP6QB8PT6BsRFWlOVwnsnYWakczLO4vXssTwwIfzuiqlAdf27Zts2EueksOeRFAW7uFsvDfeNwl2M1iGXb1X4JrKgequO5JUQkkwS0FPJlUzmFTdedKjSP0XBqCrqqkOhWebhv3El78kpj2za3L8/kg22Bcvc/np9I60pW1p2xO5+Hfslif6550nNvDK/HVVVYefRwnkk9p1rs4spj2HT94jAZXitofdj+vDCdWXs8PNYvjn/2jJwCOxD6cys508+YmWnkmzYuDd4bXZ9zW1Z+Vj4UbNvmhp+P8sWOwE2TwQ2dPNovjqGNXWT5LO5ekcmXBTdUGkapRdWa29TRuKV7LFsyDL7elUeWL/A137qOxuILGgY1Cd2dbTBqZipZPpuH+8ZxdwQVdDrR9iw/M3d7uKlbTFCr70aS6vpza3+OwaubcrioTVRQb/4JESzV9dwSIlJJAloK+bKpHNu2GTUzjV8z/Cc9pyvwYN84bu8ee8pKmP/ZlM0ja47h1mD2OSdXSqyMTK/F7myDXdmBmdPWsRqXnKJtSlV5Yk0WL2/K4dK2UUwbdeo2DWVJyzfp8vlhLGDL5Y2rrMVLRYXj3Jq5O583tuTwYN84Roa53+fpyvVbvLk1lx71HZzZ/ORiIZ/vyOOu5ZnkGDbNYzTu7V2HK9sfL1zkMWzm7vfw3PpjJGUanNPCzSfjSq4MfLryDIvx3x1hc4afc1q4+XhcfZmRCiP5uSVE1ZBzS4jgqrIEdNq0aUyZMoWUlBQ6d+7Ms88+y9ChQ0s9funSpTz00EMkJyfTuHFjbr/9dq699tqqCK1c5Mum8vyWzYFcE8Oy8Vvgs2w+35HHG1tyARjW2MnUEfE0L2Uv1q/pPsbOSsOwi7dRqIn25Rj0+ioFFdh8eWMaVzBpzPVbTPwxnaWHfZzVws3nZ0Re1T45t4Jvb47B+iN+zm7hLrWi74kzlU/2j+O2HpWbqVyR4uW+lVn8muGnbR2NhUGeWRWnT84tIaqGnFtCBFeVXC1Mnz6d+++/n7vuuoslS5YwcOBALrvsMvbt21fi8bt37+byyy9n4MCBLFmyhDvvvJN7772XGTNmVEV4IkQcqkLrOjrt6zroEu+gV4KTZwbW4+vxCTSMUll22MfwGaksOOA56bU+0+YfSzMxbLi+c0yNTj4BWsTqnNvCjWHD+7/lVmiMbL/FpfMDyWfjKJVnaug+N3GylrE6E1pHldlOpnUdvajy6xNrj7H88MnVam3bZk+2wVc787h3ZSZnfZfGXxam815yLruzA70Y9+cY/P2nDM6Zc4RfM/w0iw7saZbkUwghhBDlUSUzoOPGjaNbt25MmTKl6LG+ffsyYcIEHnvssZOOf+yxx5g1axbr1q0reuzWW28lOTmZ+fPnBzu8cpG7XVUrLd/klqVHmbvfi1OFj8YmML7F8cIlz6w/xr83ZNO6jsbSCQ2D1solkv100MuEuUdoFKXy9fgGZPkssnwWeYbNqCYuEsvoWXjMZ3HZ/HRWpfpoGq0y6+xE2tWNzCqfcm6F16Ors5iyOYfGUSpLJjTErQV6Zf6wz8OiAx4O51ulvrZNHY2U/MD/SbcGt/Wow+3dY4mpBedndSDnlhBVQ84tIYIr6FeoPp+PDRs2cOuttxZ7fOzYsaxatarE1/zyyy+MHTu22GPjxo3j008/xe/343BUfQsBEVqJURqfnZHA/auymJqUyzUL04uS0A1HfLy4MRuA14fH14rkE2BkEyed6+kkZxoMn5Fa7LlGUSpfjW9AjxLaaWR6LS6df4Q1aX6ax2jMOrtBiX1OhQB4pF8cq9N8rEjxMWpmKkc8Fv4Tcs54l8LARCcDGrro28DB3hyThQc8/HTIy67sQOGui1pH8UT/OFpVsiCYEEIIIWqfoF89pKenY5omiYmJxR5PTEwkNTW1xNekpqYyevTok443DIP09HQaN25c4uu2b98elJhLU9XjC7iuPmQ2cfD5IQdXLzjCM519vLnHgWmrXNHUT8PsvWzPDneUoXN9E42XPQ4cKsTpNnU0SPMp/JYLZ89OYXIXL/3rHc8WlmWoPLfDyWGvSlOXxetd8jFSstmeEsYPUQ5yboXXIy0VrslwcyjPQsWmd5zF8Pomw+JN2kXbKErBMvA8aKHCsBbwYHNIzlFxqTbtY/LwHU5n++Hwfg5xMjm3hKgacm4JcXrKWjVQZbev/1hh0bbtMqsulnR8SY+fqCqXQ8hyi9B5s4NN3Kos3k7K5Z6kQIXStnU0XhrXpMa2SyhNhw5w3eDij3lNmxuXHOWb3fncvtXN1JHxjGji4oFVWUUtOHolOPhobH1alFLQKZLIuRV+HYAfWxpsyvAzvLGTBHf5il51rtqwRCXJuSVE1ZBzS4jgCvrVakJCApqmnTTbeeTIkZNmRQs1bNiwxON1Xad+/cq1pBCRT1EU/j2oLtjwdnIuCvDGiPhal3yWxqUpvDM6noarVKYm5XLt4qPEORWyfDZRmsKDfepwU7dY9FO0tBHiRG3jdNrKUm0hhBBChFjQr/CdTie9e/dm0aJFxR5ftGgRgwYNKvE1AwcOZPHixScd36dPH9n/WUsoisK/B9dlyrB6fDC2PoMbVa9ejVVNVRSeG1SXx/rFYQNZPpvRTV2suLght/aoI8mnEEIIIYSoFqrk9vfNN9/MDTfcQL9+/Rg0aBDvvvsuhw8fZtKkSQDccMMNAEydOhWASZMm8fbbb3P//fczadIkVq1axSeffMK0adOqIjwRoRRF4S8dY8IdRsRSFIV/9qxDrwQHeYbNeS3dZS5RF0IIIYQQItJUSQJ6ySWXkJGRwQsvvEBKSgpdunThiy++oGXLlgDs37+/2PGtW7fmiy++4MEHH+Tdd9+lcePGPP/880yYMKEqwhOiWhvbzH3qg4QQQgghhIhAVdIHtCaQDedCVA05t4SoGnJuCVE15NwSIrikyosQQgghhBBCiJCQBFQIIYQQQgghREhIAiqEEEIIIYQQIiQkARVCCCGEEEIIERKSgAohhBBCCCGECAlJQIUQQgghhBBChIQkoEIIIYQQQgghQkISUCGEEEIIIYQQISEJqBBCCCGEEEKIkJAEVAghhBBCCCFESEgCKoQQQgghhBAiJCQBFUIIIYQQQggREpKACiGEEEIIIYQICUlAhRBCCCGEEEKEhCSgQgghhBBCCCFCQhJQIYQQQgghhBAhIQmoEEIIIYQQQoiQkARUCCGEEEIIIURISAIqhBBCCCGEECIkJAEVQgghhBBCCBESkoAKIYQQQgghhAgJSUCFEEIIIYQQQoSEJKBCCCGEEEIIIUJCElAhhBBCCCGEECEhCagQQgghhBBCiJCQBFQIIYQQQgghREhIAiqEEEIIIYQQIiQkARVCCCGEEEIIERKSgAohhBBCCCGECAlJQIUQQgghhBBChIQkoEIIIYQQQgghQkISUCGEEEIIIYQQISEJqBBCCCGEEEKIkJAEVAghhBBCCCFESEgCKoQQQgghhBAiJCQBFUIIIYQQQggREpKACiGEEEIIIYQICUlAhRBCCCGEEEKEhCSgQgghhBBCCCFCQhJQIYQQQgghhBAhIQmoEEIIIYQQQoiQkARUCCGEEEIIIURISAIqhBBCCCGEECIkJAEVQgghhBBCCBESkoAKIYQQQgghhAgJSUCFEEIIIYQQAtBW/4S667dwh1Gj6eEOQAghhBBCCCHCTUnZT9Rrj2HHxJH70mfgjg53SDWSzIAKIYQQQgghaj113y4AlNxjOBbPDnM0NZckoEIIIYQQQohaTz28t+j3ju+/AL8vjNHUXJKACiGEEEIIIWo99dC+47/PPIK+bF4Yo6m5JAEVQgghhBBC1Hrq4UAC6h91PgDOOZ+CZYYzpBpJElAhhBBCCCFE7WbbqIcCS3B9E/6CldgUNeUA+uqfwhxYzSMJqBBCCCGEEKJ2y85Cyc3Gdkdj10/Ed94VADhmfwy2HebgahZJQIUQQgghhBC1WmEBIqtJC1AUjGFnYdWtj7Z3B9qvv4Q5uppFElAhhBBCCCFErVZYgMhq3CLwgNOF/+zLA7+d/XG4wqqRJAEVQgghhBBC1GqF+z+tJi2LHvOPuRA7OhZt26+ou34LV2g1jiSgQgghhBBCiFqtaAb0hASUqGj8w84CQF82Nxxh1UiSgAohhBBCCCFqtcIWLHbhEtwCxvBAAupYuQAMf8jjqokkARVCCCGEEELUXoaBknYQW1GwGjcv9pTVqgNms9Yo2Vlov64KU4A1iySgQgghhBBCiFpLST2AYprYCQ3B6frDkwrG8LMBcCybF4boah5JQIUQQgghhBC1VuHy22L7P09gDDkDW1HR1i+HnKxQhlYjSQIqhBBCCCGEqLWOt2ApOQG14xtgdu+HYhroqxaFMrQaSRJQIYQQQgghRK11fAa0RanHGMMKluEulWq4lSUJqBBCCCGEEKLWKuwB+scKuCcy+g7Ddkej7UxCObgnVKHVSJKACiGEEEIIIWqtwgS0tD2gALjcGANHA1KMqLIkARVCCCGEEELUTjlZKDnHsN1R2PENyjzUX1ANV18+DywzFNHVSJKACiGEEEIIIWqlogJEjVqAopR5rNWhO1ZiE9SMNLSk9aEIr0aSBFQIIYQQQghRKxUloGUUIDp+sFo0C+qYNz14QVgmrrefxfXGE6j7dwZv3AglCagQQgghhBCiVirX/s8TGGMvxHY40TcsRzmwOygx6CsW4Fg6F8eqRUQ9fB2ut59FOXI4KGNHIklAhRBCCCGEELWSerigAm55ZkABOy4eY8Q5ADh/+KLyARgGzm/fD/y2a19QNRxL5xJ9359xfjUNbLvy7xFhgp6Aer1e7rnnHtq2bUvTpk254oorOHDgQJmveemllxgzZgwtWrSgXbt2TJw4ka1btwY7NCGEEEIIIYQoUrQEt4wWLH/kO/sybEVFXzYP5eiRSr2/vvQH1NSDWI2a47n73+Q99wH+IWegGH6csz5C3bapUuNHoqAnoA888ACzZs3inXfeYc6cOWRnZzNx4kRMs/RKUUuXLuW6665j7ty5zJw5E13Xueiiizh69GiwwxNCCCGEEEIIMAyU1IMAWI2bl/tldqPmmP1HoJgGjnlfV/z9/T6cMz4AwHfxJNB07IZN8d74MP5hZwHHlwjXJEFNQLOysvjwww958sknGTNmDL1792bq1Kls2bKFxYsXl/q66dOnc80119C1a1e6devG1KlTOXLkCCtXrgxmeEIIIYQQQggBgHLkEIppYCU0AlfUab3Wd+6VADgWzYS8nJMPKMfSWcfi2agZqZjN22AMGlPsOatRMwDUggS5JtGDOdiGDRvw+/2MHTu26LHmzZvTqVMnVq1axbhx48o1Tk5ODpZlUa9evWCGJ4QQQgghhBBAxZbfFrLadsbo3Bs9eQOOxbPxn3sFANqWNTg//S/q4X3YiU2wGjYN/GraCmPgGIipExjA68Ex6yMAfBdfC2rxeUE7sQlA0QxtTRLUBDQ1NRVN00hISCj2eGJiIqmpqeUe5/7776dHjx4MHDiwzOO2b99eoTjLq6rHF6K2knNLiKoh55YQVUPOrZqp8boVRAEZ0XEcqMC/cVzvkbRL3oAy5zP2JjSnycLpxCavK3peObgH9eCeoj+bH79Oeu9hpA08g3q/rSc2K4O8xi35La4R/OH9o70mnQD//l3V8v9fhw4dSn2uXAnoU089xeTJk8s8ZtasWaU+Z9s2yikauxZ68MEHWblyJT/88AOappV5bFkfrLK2b99epeMLUVvJuSVE1ZBzS4iqIedWzRX1/mYA6owYX7F/4/btMZfOwrl/F13++yiKbWG73Pgm/AX/qPNQM9JQUg+iph5E27wGfcsaGq5eSOKaxaAH0jDlqpvp0LHjSUMrDRPgfYg6llHj/v+VKwG96aabuPzyy8s8pnnz5qxevRrTNElPT6dBgwZFzx05coShQ4ee8n0eeOABpk+fzqxZs2jdunV5QhNCCCGEEEKI06Ic2I22fxd2dCxmt34VHETBf+6VaG89g2Jb+AeNwXfFTdj1GwJgxdaFlu0xAf+5V6Du3YFj7hfoKxag+H2Y7btj9ix5xacdF4/tcqPkZkNu9vGluzVAuRLQhISEk5bVlqR37944HA4WLVrEZZddBsCBAwf47bffGDRoUJmvve+++5g+fTqzZ8+mYwl3AYQQQgghhIgo+Xk4Fs/C7NgTq12XcEcjToP+y2IAjH4jQHdUeBxjyBl4TBOrUTOsTj3LPNZq2Q7v9Q/gu/R6tPXLMPsMg9JWiSoKVmJTtP07A21a2nSqcIyRJqh7QOvWrcuf//xnHn30URITE4mPj+ehhx6iW7dujB49uui4AQMGcP311/N///d/ANx99918/vnnfPTRR9SrV4+UlBQAYmJiiI2NDWaIQgghhBCiFtDW/oy2bRNKzrHAr9xjYIPZsTtm136YHXuAy13h8dXtm3FPfQY17SBW3XjyJn8GTlcQP4GoSkUJ6MDRlRtIVTFGnnNaL7HjG2CMnXDq4xo2gf07UdIOgSSgpXvmmWfQNI1Jkybh8XgYOXIkb775ZrH9nNu3byc9Pb3oz9OmTQNgwoTi/xD33XcfDzzwQLBDFEIIIYQQNZXPi+vDV3EsmVPi09rvm2HOZ9i6A7NDd3zX3IbVvE35xzf8OL/9H47Zn6DYFgBq1lH0ZXMxxlwYjE8gqpi6fxfawd3YMXUwu1Zw+W0IWIlNAVDTDmKGOZZgCnoC6na7eeGFF3jhhRdKPSYzM7PMPwshhCjFsUxcn74Orii8f7njpLLtQghRmylph3D/5zG0PduwHU78516BldAIOzYOOyYOxe9FS1qPtmUt6p7t6EnrUd56hvwn3ip9KeSJ46en4n714cD4ioLvvKuwmrXG/dYzOOd8hjHqPFDLLqIpwk9fvRgoXH4b9HQoaApbsaiph8IcSXBF7t+4EEKIYtTtm3G//jjq0SMAWM1a4z/zkjBHJYQQkUHbuBL31KdRcrOxEpviue1JrJbtTzrO7FFQ9OVYJtGPXIe2ZzvauqWY/Uac8j1cH7yCtmcbVoPGeP7vwcCeP9PA+vZ91NSD6KuXYAwaE+yPJoLJtk9YfhvZ/1ZWw2YAKGk1qxeo3DoXQohIZ9s4fviSqGdvRz16BKtJSwCcX0xFSdkf5uCEECL81N+34H75AZTcbIzeQ8h7YmqJyWcxcfXwn381AM5v3wfLKvs9tv2KvmE5tstN/iOvHy84o+n4zpkIgOO7T8C2K/txRBVSD+xCPbgHOzYOs0ufcIdTJqth4QyoJKBCCCFCxfDjfv1xXJ++jmKa+M6+nLyn3sU/5AwUnxf328+BVYN2hvi8OD99A33p3HBHIoSoRpw/fIFi2/hHX4Dn9qfL3bLCP+o8rPgGaHt3oK39ufQDbRvXF28FXnP2ROx6xbtDGMPPxqobH5hN3bK2wp9DVD39l5+AyF9+C2AnNMJWFJT0FDCMcIcTNJH9ty6EELWcvmwe+uqfsKNi8Pz9Psz+IwHwXnMb2tZ1aNs345j3Nf6zy+7VXC0YBu7/Pom+bhm2w4nRZ2iN6nsmhKgaSkYq2tqfsVUV34S/nN7eeKcL3wXX4P7gFZzfvk9+vxElvl5bvxxt+2bsOnXxnVPC963ThX/8pbi+fBvHd59gdu9fiU8kysMx80Oc877CatISs1VHrNYdA7PeigK5x1ByslFyj2E3aByY6VTVguW3i4DIX34LgNOFHd8ANSMNJSMVu2HTcEcUFJKACiFEBCvcp+K94qai5BOA2Di8195N1MsP4vxqGkbPQdhNW4UnyGCwLFzTnkNftwwAxe/DsWwu/vGXhjkwIUSkcyyejWJZ+AeMxq6feNqvN0aeizX7E7T9u9BX/3TyHk7LwvnV2wD4LvwzRMWUOI5/zIU4Z32MvnUd6s5krLadTzsWUT6O7z/H9fU7AGjZm9C2bSrzeKthU/xjLsRq0wn10N6C5be9QxFqpdmJTSEjLVAJt4YkoLIEVwghIlV2JtrWtdiqitH/5OIYZu+h+IefjeL34X77OZSDe6rn3iPbxvXBKzhW/IjtjsJXsCfLsXBm9fw8Quq4PsAAACAASURBVIjQMfzoi2cB4D/jooqN4XDiu/AaoHAvaPFtDfU3rUA7sBurQWP8ZbVZiamDv6C3o/O7TyoWizglffFsXJ/9FwDP3+4k/67n8V76d4z+I7EaNcds1hqzY0+MPsPwDx2PldAINfUgrs/fJOq5fwJg9B8FWvWYh7MKkk6lBu0DrR5/80IIUQvpa5eiWBZGjwEQW7fEY7xX3Yy2ZQ3aziRiHvgrVkIjzB4DMXoMxOw1CBzOEEd9mmwb5xdTcSyaie1w4LnjGcwOPdB//h710F7U337F6twr3FEKISKUvnoJatZRzGatsTpV/LvCGHEO1uyPUQ/uQV86D2P4WYElmz4vTX6aCYDvkmtP+Z3qP+tSHPO+Qlv7M8qxo9hx8RWOqVbJzcax4kesJi0w23aFqOgSD9NXLcT1/otAYCtKYd9Vs+cg/KWNbZloG1fhWDQT7ddVgb3CQ8+sgg9RNawa2IpFElAhhIhQRWXiB4wu/aCYOuTfMxnnrI/QNq9BTU9BXTwLx+JZWIlN8U68IbB0txz97cJBX7kQ55zPsDUNzy1PFFUkNEadh3PmhzgWzcQrCagQohSOBd8A4D/j4sp9z+kOfBf8Gfd7k3G/8zz2h68EZp5cbrRjGZjN22IMGXfKYex6CVjtu6Ilb0TdmYTZe2jFY6om1H070RfPQsnNRsnPRcnLBcOP2WMg/rEXnlSw6SS2jXvq0+gbVwb+qKhYLdpiduiOHZ8YKBSkO8CTh/Ob91BsG++frit/GzJVw+wzFLPPUJS0QyjHMrHadankpw6dwn2fag1qxSIJqBBCRKLsTLSkddiahtFveJmH2s1a473xYbAs1D3b0Tb9gmP5fNRDe4l67THMTr3wXvkPrDadQhR8OVkWjlkfAuC9+tZiF2r+UefhmPUR+poleI9lQly9cEUphIhQ6p7tgcJAUTEYQZjRMoafjX/LWrTkDajHjqLt31X0nO+y60HVyjWO2bYLWvJGtJ3JNT4BVdJTiHr2DpTcYyc9p+1MwjH7Y4yBo/Gf+adSkz5tzRL0jSux3dFYTVqi7t2Otvd3tL2/l3i879wr8F9wTYXitRObYBfMKFYXhTOgisyACiGEqErlWX57ElXFatMJq00n/OddGdgnM/1dtN82EvXEjfgm/BX/xX+r0rhPh/brqsC+qvgGGKPOK/ac3aAxZs9B6BtX4lj6A/5zryh5EK8HJSMVNTMdq0nLU99pF0LUGI4F3wLgH342uEtesnladB3vzY8Ffp+fi3p4P2rKfg5kHKVR7yHlHsYsKD6k7kyufEyRrKBNmJJ7DKNLH4wR52BHRQeKNPl8OJZ8h7Z2KY4VP+JY8SNG3+F4bnoEnK7jY+Tl4PpoCgDey2/AGDcBvB60nUmoO5NQcnPANMDwo5gGZsv2gWW3EbqqpyrIDKgQQoiQKFp+W9Ey8ZqOMe4ijMHjAktZ536Fc9aHgSVLsXHBC7QSnN9/BhCodKs7TnreP+bCQAK6eFagzUxhCf2lP+CY/w3qkcPF7rrbqorZczD+kedg9hoS8f3dhBCVkJuNvuJHAPzjJgR//KiYoht6x7Zvp9FpvNRqE0hAtZ3JgUJqNTRZcn72JtqOJKz6DfHc8vhJN0vNXoNQ0g7hWDgDx6JZ6OuW4n7tMTy3Plm0l9b51TTUzHTMdl0xxlwQeKHLjdmlT9GWjNrOrlMP2x2FkpcDOcci5md4ZUgVXFF1DD9KyoHAevv0FJSMVMjPDXdUQkS+Yycsv+1b9vLbU4qpg+/Kf2B27YtimuhrlgQnxkpSd2xFS96IHRWDv/Ci4w/MngOx6ieiphxAS1qHknIA97/vwj3tebQ92wL93XQHVmJTzDadQVHQNywnasojRN9xKY5ZH4X4UwkhQsUxfzqKz4vRrT92k5bhDqcYO6ERVlw8Su6xGlW59ETaL4txzv8aW9NLTD4L2YlN8E28kfwHp2DHxqFvXIn7tcfA70P9fQuOhTOwNQ3vpLtPr39rbaIoWIk1axZUbg+LqmHbRD35D7Q924s/rGnkP/AqVofuYQpMiMinr/25YPntwKDd6TQGj0XfsgZ91UKM0ecHZczKcM4pmP0ce2GpPfXQdPwjz8P17fu4PnwVJT0VxefFjo0L9EXtNRg7tm7RRYuSlYG+fD76z9+jHdiN66tpGEPPxE44nbkLIUSk01YvDrRLAfznTAxvMCVRFKy2nVE3rEDblYzRqFm4Iwoq5fA+3O/8GwDfFTdhtet6ytdYLduRf99LRD13J/qGFbhffwLlyGEU28Z39uVYLdpWddjVmp3YBPbtQE09VDTDXp3JrQZRJZSjR9D2bMdWVawGjbDqN8SOiUMxTZyzpTeWEGXRVy8GKrH8tgRGvxHYmo6WtAElKyNo41aEcng/2tqfsXUH/jP/VOaxxqjzsFUV9dA+FJ8X/9AzyX32g8Beo7j4YnfM7br18Z8zkfyn3wvsnQW037dW6WcRQoSWmrwR99SnA5VQL70es+BcjzRmm2qyD9TvA09e2cd48lCTN+L4/nNcbzxJ1NO3oXjy8A8YXf5KtIDVsj35972IHVMHff0ytH07sBKb4Jvw10p+iJqvqBeozIAKUTp19zYAzM698dz3EgDKsaNE33k52sYVKCn7sRs1D2eIQkSmY5loW9cXLL8dFrxxY+pg9hiAvmEF+uqfAi0LwsT5w+dFfdjs+AZlHmvXT8R/3lVom9fg+9O1mD0GnvoNFCXQS3TTatQdW2FQ8BJ5IUT4qPt3EfXqQyh+P75xF+E//6pwh1Qqq23hPtCkMEdSBk8eUf+6GfXgHqx2XTF6DsLsOQirWWvUHUnoW9eibVkbKAZkWcVearZsj/e6e057f6vVqgP590wm6t93oeTl4P3LHeByB/NT1UiFCWhN6QUqCaioEtru3wCwWh9v+2DHxWMMPgPHz9/jmP8NvmtuDVd4QkQsfe3PKLaF0W1Q0AsNGIPGBhLQVQvDloAqWRnoS38AwFfOpXO+S/8Ol/79tN6ncEmYtkNmQIWoCZT0VNwv3ouSl4PRb0TgGiKCi/sUVcLdsz1QxVWLvEtu18evFbWa0bZvRtu+Gb5+B1tRUezjCaetqpitOmK16YTZphNW285YzVpX+DNZbTqR9/R7KJnpRYm6KFth65iImwG1bdSdSegrF6JmpGJ0H4DZb3hghVIZIu9sEDVC4Qyo1bpjscf94/8USEB//h7fn64tfe+XELWUvnIBAMbA0UEf2+gzDNvhRNu2CSU9FTuhYdDfoyzqvp04v34Hxe/H6DsMu2mrKnsvs21nbEVB3bMtsMSsoOKiEKJ60JfNQ9u+GSVlf6AdSkYqAGaH7nhufLjcPTnDJrYuVsOmqKkHUQ/sxmrZPtwRFaOtXoxjyRxsh4P8+19BycxA/3UV2qZVqBlpmM1aY3brF/jVqVfQr9fs+onY9RODOmZNdnwGNEwJqGFAXg5Kfi6KJw8lNxtty1r0VQtR047PyuprlmD/72XMTj3xPPBKqcNJAiqCz7ZRC2ZAzT80vrdatsfo3Bs9eQOOn78PtF8QQgCgZKSi/bYR2+HA6Dci+G8QFY3Zewj66p/QVy8OtDapSpYF3nz09ctxLJwRuLsO2LoD3/kVayJebtGxWE1aoR3cjbp3R6kN0IUQkUfdlYz7rWeKPWZrGmanXnhufrx4H8kIZrbpHEhAdyZHVAKqpKfifncyAL6JN2G17waA2X9EoG2MNz84fVVF0NgJjbAVBSU9NZAMhqrNWE4Wzpkf4Vg4A8XvK/EQq14CxsAxWE1boq9fjrZ5DXryhjKHlQRUlEjdvxM7tm6FmrorR9NQs45ix9QpWjJwIv/4PwUS0HnTA8sAI/0uphAhoq9ciGLbGL2HQnRslbyHf9CYQAK6cmHpCWheDlryRrTfNoLLjdWkJVbTVliNm4MrqtSxtaT1OD98FfVoGvh8KIa/2PO2Oxr/sPH4x12E3ax1ED9Vyaz2XdEO7kbbsVUSUCGqEW37FgCMLn3wnzMRq1Fz7AaNq11vX6ttF1i1EG1nUkRUHwfAMnG/9XRgKXOvwSdvx1AUST4jkcOJHZ+ImpGKkp6C3agZ5GbjWDwbdf8ulMwjqJnpKJlHsGPq4r3iRsz+I08ex7ZR92zHjorGbtis9GXsPi+OeV/h/O4TlLxAC0U7Ng47KgY7Khrc0VjNWmMMGovZqWfRtbwx5sJAj94NK8r8ONXrTBYhoe5IIuqpm7EbNSPvmfdPO0EsKkDUqkOJ/7HNPkOxEpugph1E27ASM5iFVoSoxvQV8wHwDzmjyt7D7DkY2x2FtisZJeVA4IcYoBw5jGPJnFILThS9vlVHfFfedFKDcH3BDFwfT0ExzWKP204XVtNW+EdfgDFkXEgvbMx2XXEsmRMoRETZ1XaFEJFD3RWoHGsMGI3Za3CYo6m4on2gEVQJ1/HdZ2jJG7HqxuP9+30RvY9WFGc1bIqakYq6Zzvq8vk4531ZlByeSMnLJeo/j2L0HY73z7cHljpbJvrqn3DM/gRt7++B8eolYHbogdWpJ1Z8g4IENvBL27IGNSMNAKNbf3wTb8Bq1aF8gcbUwRg2vsxDJAEVxdk2rk9eQ7EslEP70NYuxRww6rSG0Ar3f/5h+W0RVcN/xiW4Pn0dx/yvJQEVgsCqA23vDuzoWMyeg6rujVxujD7DcKz4Ef2XRRjDzsI56yP0n75DMQ2goOBEh+6YXfuCZaEe2otycC9qyn60PduIeu6f+AePw3fFTdh16uH85DWcC74FwHfulfjOvyqw59LhDOvFjRQiEqJ60goStupeoMZq1SHQRurArsCy1jJWkISCun8nzm/eBcD79/tPWShGRBa7YVNI3kDU648XPWZ07YsxeFxgT229Blh166OvXozri7fQ1y1F27oO/5gL0Nf+XLR/1IqLR7Et1Mx01NWLoaD12x+ZrTrgu/wGzO79g/5ZJAEVxeirFqL9viWwzty2cX7/Gfn9R57WRaS6q2D/Z+tSElDAP/IcnN+8i751XWB/Vst2lY5diOpMX/4jUND7s4oL5hiDx+JY8SPO77/AOeN/KH4/tqLgHzwOY8i40gtO+Lw4vv8c56yPcKxcgL5hOVbjFmi7t2HrDrzX3nPKu56hZDVrhe2OQk07hJKVgV23frhDEkKcSm426uF92LoDq0XbcEdTOS43VvM2aHt3oO7ZjtWxZ1jDcX75Nopp4h9zYdXe6BRVwipYsQRgdO6N7+JJWJ17nXScMe4izD5DcX34Kvq6ZTi//zzw+sSm+M67AmPYWeBwohzai7ZtE9pvv6Lk5WDHJ2DVa4BdLwG7YVPMzr2L9doOJklAxXE+L87PpwZ+e9XNOL/9AG1HEur2TeX/0rTtUivgFhMdi3/42Th//AbXx1PIv/N56QMlai/LKqp+W5XLbwuZ3QdgR8ei5B4LvOeA0fgu/tup92U6Xfgn/AVj6Jm4PnkNfd0ytN3bsOrG47ntqaJCFhFD1TDbdgnc6NqRJKsthKgGilZRtWwPuiPM0VSe1aYL2t4daDuTw5qAqskb0TeswHZH4btkUtjiEBVnjDwXJTcHs+fAk7bB/JFdvyGe255CW7MEx8oFGP1HYQwcVax1jt20FUbTVmHZnywJqCji+P5z1IxUzJbt8J9xMUp2Fs6ZH+Kc8zmecn5pKhlpqMdKL0B0Iv+5V6Kv/gkteSPuVx/Cc8cz1aaynRDBpG7fjJqeglW/IVbHHlX/hroDz7X3oG9Zi3/shNNegWAnNsFz+9NoG1ehbf4F/9kTQ97Spbysdl1h6zq0HVslARWiGijcL2lW8+W3hcy2nXH8NBt1Z1LQx1bSU1BTDoDPC34vis+H1aAxVqc/XLPZNq4vCiYYzp4oS2+rKTsuHt/EG8r/AkXBHDDqtLfShYIkoAIA5egRnLM/AcB31S0F+zQvxvH9Z+jrl6Ec3FOunn1F7Vdadzzlsl07oSH5979M1HN3oG9Zi/vVh/Hc/pQkoaJ6sExcbz2LHZ+I7/L/q9ReR0dB8SFjyLgqW+7yR8H4oWT2GoTZK7KXcZkF+0BV2QcqRLWgFRQgstrUjAS0cB+rtvO3oI6rpB0i+sG/ofi8Jz3nvXgS/ov+WvRnbe3PgWrgcfH4z6ni9ltClENornRExHN+9TaKz4PRb0TRtL5dtz7GsLMDz//wZbnGKVo6U8b+zxPZTVuRf9/LWHHx6JtX457ySOBOnhARTt23M7CPcs6nOGZ9VPGBDD/6L4sDvx1yZnCCE0UK269oO5PAMk9xNIEeeEKIsCmcKawpM6BWs9bYThdq2kHIzgzauM6ZH6L4vFiNmmH0HITRfyT+AaOxFRXXN+/hnP5u4PvMNHB9+TYAvov+Ki1WRESQBFSgbV6DY+lcbE3HO/HGYs/5zr4MW1HQl89Fyco45VhFBYjalLH/8w/sZq3x3PciVp166Jt+wTXtudP7AEKEgVpQxhzA9fU7aGuWVGgc7ddVKLnZmM3bVv+CGxHIjovHSmyK4vWg7t9d+oE+L1EPX0fUv/4hN8GECBMlMx316BFsdzR24xbhDic4NL2ofYXzm/dRMtMrPaSSsh996Q/Yqkr+nc/juet5PLc+ifeWx/He8BC2quKc8QHOL99GXzIH9fC+QKI6KkJ6kYpaTxLQ2sy2ccz9EveL9wLgP/uyop6ARYc0aYnZZyiK34/jx29OOZ56mjOghazmbfHc/xK2pgdmg/JP7mskRCQpTECtJi0BcE99BnXP9lO/0JOHunsb2pqfcfzwJc4ZHwBgDJXZz6pitj/1MlzHoplo+3ag7UjC+c17oQpNCHGCov2fbTqFbDtCKPgLvt+dC74l+q4rcE17HnXfzgqP55zxIYplYQw7C7tx82LPGUPG4bnpUWxNw/ndJ7g+nAKA709/B1123onIIP8TayuvB9d7k3GsCLR+8J13Jb5L/17iob5zrkBftwzHgm8xegwotYqbkpGGmp2JHROH3aDxaYdkNW+L1aoD2s4ktJ3JmN36nfYYQoSKtieQgHqvvBl91UIcy+bifuVB8h97E7teQsmvSVqP+9WHUf5wg8XWNIzB46o85trKatcVVvyItmMrxpgLTj7A68Hx3SdFf3R8/zlG3+FYHbqHMEohhFaw/La69//8I2PMheQ1a4Pzhy/Q1i/D8fP3OH7+HltVQdUCvzQNs1MvPLc9WaxS6R8ph/aiL5+PrWn4LvxziceYA0fjUTXcbzyBYhqYbTpjDBxdRZ9OiNNXc24viXJT0g4R9dQtOFb8iO1yk3/L4/guvyHwBVgCq0N3jG79UXKziX76NlzvvQi52Scdd7z/56kLEJXGLNivVRXV4oQIGts+PgPaqj3eSXdhtu+OmpGG+9WH4djJ+3zUbZtwv/wASn4uVqPmGL0G4xt3Ed6JN5L/4JSIrSJbExQWItJKmQF1LJqJmnUUs3VHfOddiWLbuN9+Dryesge2bbRNv6Ac3BPskIWolY5v46lZCSiKgtWpJ57bnyLv+Q/xnXkJtjsaxbJQDD+Kz4OSn4u+YTmO+dPLHMo54wMU28IYfg52w6alHmf2H4Hn9qcxeg7Ce+3dlSqUJ0SwyQxoLaP+voWoVx5Eyc7CatQcz23/wmrepuwXKQqeO54ONJ//7lMci2ehrV+K76pbMAaNLfpS0woq4JbZ//MUrHZdYf50tB1J+Cs8ihBVSzlyOJBI1o0vmu303P4voh6/EW1nEtEPT8J73f1FFWLVHUlEvXgfiteDf+h4vNffX6OWl0U6q2U7bIcD9eCewM2zmDrHn/Tm4/juUwB8F0/C7NYPbeNKtP27cH71Nr6rby150LwcXO9OxrF6MbY7ivz7X64xVTuFCAvbPl4Bt4bNgJ7IbtQc3zW3Bb5bLBMsCywTbfMaoqY8gvPrdzH6jSixlZ1ycA/6ygXYmo7vwmtO+V7VoVK5qJ3kCqgW0VctIuq5O1CyszB6DCDvsf+eOvks5HTh+9N15P1rGmaH7qhZR3H/91+4n78Tde8O4IQWLG1Ob//nicy2BTOgO7ZKNUoRsdSC5bdWyw5Fj9lx8eQ/NAWzUy/UrKNEvXQfzg9eQd2+majJ96B48vAPGoP37/dK8hlqugOrVeB7ybFsbrGnHAtmoB47itm2C2avweBw4r3+gUARj3lfoyZvOGk4dWcy0Y9ej2P1YgAUT37gBsOhvVX+UYSoqZTUAyi52YEbe/VrwYoQRQkstXU4wRWF2W8E/kFjUHweXP97ucRrIOe376PYNsao8yq01UmISCFXQbWBbeOY/XFgL4Dfj3/MBXj++WzxWYDyDtWsNfkPTsEz6W7smDj0pPVEPXo9zg9eQdtV+RlQu2FT7Dp1UY8dRTlyuMLjCFGVtL2BYkNWy/bFHrcTGpF//0t4L78BW9MDBSeeugUlLwej73C8//dQmXt7RNXxDz0DANfHr+H85HUwDfDk4ZxTMPt50d+KVnNYrTvivyCwt8o99WmcH7+GY85n6Mvn45j1MVFP3YKadgizVQdyn3kfo8cAlOwsol64ByUjNSyfT4jqrrBPptWmc61dLuq76hbs6Fj0Tb+gr1xQ7Dltw3L0XxZj6w58F1wdpgiFCA65EqoFnB+/hnP+19iKgm/ijfjPvrxyX+6qijH6fIz+I3F++z6OBd/iXPAtQIULEBVRFMy2XdA3rkTbmYRRwhIUIcKtaAa0VfsSntTwn3clZvf+uN58Gu3gboxeg/H841GpQBhGxriL8Kgqrg+n4Jz7Jeq+HVhtOqFkZ2G264LZc2Cx430XXoO2YQXanm0453110ni+My/BN/FGcDjx3PokUc/fhbZjK+4X7iX/oVchtm6oPpoQNcLx/p9dwhxJ+Nj1EvBecRPud1/A+fFrgZtbXg+uT15HL2j15Rt3Ue2YIRY1mlwN1XTZmYHkU9Px/ONRzP4jgzd2bBy+a27DGH0Bzk9eQ9+yFqPHgErfuTTbdUXfuBL1960waGyQghUieAoLEJktS0hAC1itOpD/xFTUnUlY7btL8hkBjDEXYjVrjfu1x9C3roOt64DA3s+Tvrd0B/kPvYq+bjnK0TSUzHSUzCMonnz8o8/H7Dv8+LGuKPLvfI6op29DO7ibqJceIP++F8EVFcJPJ0T1VrT/sxLbeGoCY+S5mMvnoSVvJGryvagH9qD4PNguN74Jf8V/1mXhDlGISpMrohpOTTkAgNWibXCTzxNYzdvguWcyyqG92PGJlR+v4O6nJpVwRSTKyULNSMV2uU/qm3sSpwurc+/QxCXKxerYk/zHp+Ke8ijarmTM9t0xuw8o+WBXFMaQcrbHiY3Dc88LRD19S2Am9D+P4rnjGdAdwQteiJrKNIr6KFemjkSNoCh4Jt1N9MPXFm1t8g8Yje/Kf0i1dFFjSAJawxUloKe6UK4sRcFu2iooQ5kF1e/UPdvA8MsFnIgohf0/rRbtSm1dJCKbXb8h+Q++ir5mCUb3yq/aOD5uIvn3TCbqqVvRN63G9fZzeG94SIpOCXEK6oHdKD4vVmJTqFMv3OGEnd24Bd6/3Y2+fB7+c67A7FHKTTIhqilJQGu4wgTUbljFCWgwxdTBatIS9dBe1L07anQ5dlH9FPX/LGP5ragGnC6MoWcGfVi7cQs8dz1P1HP/xLFyAXbBVoWgF1WxTECR5FZUP6aBciQF9fB+1JT9KIf3FfXoNdvW8tnPExjDz8IYfla4wxCiSkgCWsMpqSGaAQ0ys10X1EN70XZslQRURJTy7P8UtZvVphOeO57GPflenD9+g12nHv6L/lr5gW0bdcdWHEu+R1+1EKtpK/If/o9UVhaRzbJw/Dgdbet61MP7UFIPophGiYeavYaEODghRDjIT60aLmRLcIPMbNsVx9K5RVXxhIgURTOgrTqc4khRm5ld+uC56RHcrz2O65v3UDPT8V52fYXaX2HbOH78Bn3hTLSDu4se1nYmoS+fjzHinOAFLkQwWRau9ybjWDKn+MPxDbAat8Bu3ByrcQusxs2xmrbGbtg0TIEKIUJJEtAaTk2thktwAatdQSGigmU5QkQEnxf14B5sRcVq3ibc0YgIZ/Yfiffae3C9PxnHoplo65biu/pWjIGjT2tJrr5sHq6PpgBgxcVjDBuPHVMH11fTcH77P4whZ8heeRF5LBPXtH/jWDYX2+nCe/WtWG06BW6Iu6PDHZ0QIowkAa3JcrNRco4FqnXWrR/uaE6L1bwtttMVmMHNyZKeeiIiqAd2oVgWZtPW4HSFOxxRDRgjz8Fq2xnXey+i/b4Z9xtPYCz9Ae81t526inIBfdlcALwXT8J//tWBlj6WiWPZPNRDe9F//h5jzIVV+TGEOD2mgeutZwP7oF1uPP98FrNLn3BHJYSIEFK9oAZTT9z/GewCGFVN17FadwRA25Ec5mAA20ZJTwWj5H0ronZQCyvgtpL9n6L8rOZtyH9oCp6/3YUdHYP+6yqiH/grzg9eQclML/O1SmY6WtIGbE3Hf+Ylx/vJqhreS64FwDnjA/B5q/pjCFE+hh/Xf58KJJ/uKPLv/rckn0KIYmQGtAarlhVwT2C27YK2bRPajq2YvQZVeBwlIw319y2YvYec1qyVknIALWk92tZ1aMnrUbOOYrujMDv1wuzeH7NrP6xmratfcl9V8nJwffYmZre+GIPGhjuaKiEVcEWFqSrGmAsw+wzF+eVb6Mvm4VzwLY6ff8B/1qX4zr0ComNPepm++icU28LoOeSk/aNm/5GYLdqh7duBY/FsaNMzVJ+mdN58HEu+x+g9BDuxSbijESGmpOzH/d9/oe36DTsqhvy7/43Vvlu4wxJCRBhJQGswpZoWICpktu8KgLrzhH2gphH4XDF1sOPiy0z+lMP7cH73KfqyeSimgdFrMJ7b/nXqvVKmgeu9F3H8/H2xh+2oGJT8XPSNK9E3rgwc2rI93hsexGretmIfsgZxzvkMx0+zcfw0G29mOv6zLgt3SEGnyQyoqCS7XgLe6nttbwAAIABJREFU6x/Af85EnF+/g75uGc5ZH6Gv+JG8p96BqJhix+srFwBgDC7hpo6q4rvkWqJefQjH/7d33+FRlOv/x9+zsyWFEkhCT+hFIBSlC4iAlQPYQT34s4JYDjb0AIKCHbAiKH7tHqx4LAiCikiRbqEpvUiHAKEk2c3uzPz+WFjMoUOSTcLndV25YGeeefZ+ApPZO0/75j8Ydz5xjDd1IJCNsX9veDpGfg0fdxx8//ccngU/4ZnyGVlD3zi9RZekSHL//B2+91/E8GdjJ5bHf+9Q7OpaxV5EjqQEtBiLDMEtoj2gdo1wAmqu+RP3jEmYi+fjXrYQI+sAAI7Hi5NYHjuxPE7pMjjxJSGuJE58CcxVSzEXzsBwHBzDheOLwb1oLr43niZw56PgMo/+plYI39in8cz7Ecfrw2rUEuucpoTqn4tTMRVjT3q4R3TZL5hL5mP+tZrYx/uQc10fgp2vOnv35MvOxDP1y8hL34ejwZ9NsFuv4tNDbNu4NmoLFskbdpUa+Ps9hWv1MnxvjcDcsh7vt5+Sc9UtkTLGzq2Yq5fheGMINW1z1Hqspm2wqtfDXLec5IU/QWoq5opFmMsXYa79EyNjF8a+PRgHh+g6JUuT0+lKgp2vgJIJedomz/ef41nwEwCunVuJeXsE/nuGFp+fAZKb48CBvbj2pOP59hM8s78HINjiQgI3P6BfPojIMSkBLcYiQ3CLaA+oUzYZOyERV8YuYt4aHjlul03GCPgxMvdjbNuIa9vGo1/v9hA8/xJyLu+JkZ0Z3hh+3jSIiSNwy0NHfigKhfC9/iSeBT/hxMSR/eBz2HXSjogpsjm0PwvfuFfxzJiEb9yrmIvmEbj9EZwySXn+vSjsPNMmYGQdwKrTiGC7S/G9PRLff9/G8GeRc12fovEB1LYhcx+GPxvDnx3uMQrm4MTE4cTGYRzYhxHwY5dNzvMP7nL2sms1IHDLA8Q99S88kz8h2Kl7ZNE497wfAcLJpy/26BUYBjlX30rsyIepNO0LjKnjj1rM8Xhx4uJx7d2D78t38U76iGC7ywh2ugKnYuoZ//LMtXoZ3o9fAyDQ4068X3+Ae+EMPD98EZ67KsWG9+PXcC+cgZGRjhEMRo473hgCvf4V3haoKPzMF5GoUQJajBlFvAcUwyB0wT/wTP0Cq1ZDQo1aYDVsfjihzs7CtWs7xq4dGPszMLL2YxzYD1n7Ib4kwQ5dI8mgA2Tf/wyxI/vjmT4RJzaenJ59Dz8kQ0FixgzD/cvMk5+3EhNH4LaHCTVuTcw7I3AvXYBr8O1kP/kWTkJi/n1fCptgDp4pnwGQ848bw/N1fTH4xj6Fd9LHGHvSyenWC6dS1SgHehyhILFD78T8a80Ji2r+p+Q1u04jQk1a4/59Dp6vPyCnVz/gbwloq07Hvd5q2JzQOU1x//kbjseDXbM+Vr0mWHUaYSdXxCmVEElgXSsW4530Ee5Fc/FO/RLv1C9xYuKwU2pgpdbCPvRVpfrJD9Xdl0HM6McxLIucS64leHlP7KQKxI5+HO/Hr2HVqq+hmMVFdhbebz+JvHTi4rETknEqphC45vbC/XNeRAoNJaDFVXZWeNEcj6dI98jlXHVLriFpucTGhT8kneR+jHa9xvjvfYKYlwfinfwp7t9mg3lwKK4/G9fuHThxJcjuPxK7xsl/WLKatSOrVn1iXnk0PFx4+kSC3W866euLOvfP3+HK2IWVUhOrUQsAQi074vhiiHn1MTxzfsAz5wdC9ZoQ6tgdo3QFCOaEexQP7IPMfWC6wevD8cWE/yxRukC3OXFPn4T515rw/VKqLE5MLMTEgukJ94T6syA7C8OyCLW5uMDikrNHzjV3YC6ai2fahPD86VAw/H8yrgRWWvPjX2wY+Ps9xab5P1Oldfvj3jt2vcb46zXGtWkdnsmfYi6ZjytjV3jawqqlkXKO4cKpmIKVUhO7ai3slJrYqbWO/OWabRHz+hO4du/Eqt0wPOIBsFp0IGf5FXinfknM6GFkDXvjqIssSdESmdpTISX8b3qsnnkRkeNQAlpMRR4SyZXP3nmJR2E1bon/zsHEjH0K1/ZNuc45JUuT/dCIyPYvp8JJSCTnqtuIHfEQnhkTCXb959nxfbctvJM+AiDY5YZcw66sJm3Ifnwsnu8+xz1nKu7lv+Ne/juNXCYu2zpx1QmJ4Tm+SRVwkipgJx/8M7E8TlKFvEtQcwJ4v/4AAH+fR7GaX5A39YqcAjulBqHWF+GZ/R3e/76NU64SAKFm7cHjPXEFsXFkn8L+tHaV6gRufwQAY98eXH+twfXX6sNfW//CtWUDri0b4GBPLIBdqgxOQlmMQABy/BiBbIysTOxSZfDf9djhbWKAnJ59MVf/gblhJb73XiTQd/DJf0OkUIqMrKqYquRTRE6bEtBi6tBDoqjO/8xPVosOZJ7TBGNfRq7jTlL5M3qgWvXPxU4qjyt9O+Yfv2I1bHamoRZ65sKZuLZvxk6uRKjFkYmbXaUGgVv7E+jZF8/s73FP+xpz0zoc08QpUSrc0xlfEiwLcgIYOX4I+MMfiDN2QcYuzDV/HFGv43IRancZOdfcHl4N+Qx4fvwaV0Y6VtXaWOe1O6O6RM5EzlW34J4/DffcqeF7gxMPv80LTqky4a2l/v4zKyeAa/P6cDK6cQ3mhvCfrn17YN+e3NeXKEXgriE4ZZNzV+z14b/7MeIG3ox73o8EbrwXSmn+dFHm2la0V9cXkcJBCWgx5SriW7Dku5IJOHm9kIzLRbB9F3z/fRv39InFPwF1HLzffAhAzuU9wsNojyWuBMHOVxLsdAVr/lhGzfoNjr9IhRUKr965cxuu9G0Y6dvC833Tt+HaGX7tmT4R94KfyOl+M8HOV+bqeTlp/iw834wLt+GqW86OXmsptJzkigQ7dsP73ecY+zOwS5fBOqdJdILx+rCr18WuXvdvAToY6dswMveHh8v7YnC8MRATd8z7zylfGateE9xLF+BeMp/Q+RrCXpQV9dX1RaRwUAJaTLl2bAH0kChoobaX4v3iXdy/ziKwP6NYr5ZqLl2IuWEldukyhNpeenIXGQa213fiFRJNN05i+fAQXBofWc2WDfg+HI17yXx8H43G89ME/Lf2P2LV4hPxfP8Frv0ZWDXPwWrc+pSuFckPOV174ZnxLYY/i1CLC4+9ZVQ0GAZOckWc5IqndJnVuBXupQswF89TAlrERVbXr6DPFlK4hUIhMjMzox1GsRcfH4/7NDoAlIAWU0YR34KlqHISy2GlNce9eB6e2d+HFxM5llCImNefwNixlexHRxXoojtnzJ+F74OXAQhefE2Bx+5Uqor/wecwF83F9+FoXFv/IvalgWQ9/e7Jr0CcdQDvtx8DkHP1bdo2QAqHUgkErr8rvE1KpyuiHU2eCDVuiW/cKNxL5hOwQscfLSGF2qHPFvrlthRmoVCI/fv3k5CQgKFne75xHIeMjAxKlix5ykmoxpsVU5FhMkpAC1zwgi4AuKdPDG/UfQzej8fgXjAdc8PKXKtPFgW+ca/i2r4Jq0r1cAIaDYaB1aQ1WU+/QyitOUbmfnzvvnDc7/nfead8hpG5H6teY6z65+VzsCInL9ThH2QNHxfen7MYcMpXwS5fBSNzP641f0Y7HDldgWxcGek4phsnsVy0oxE5pszMTCWfBcAwDBISEk6rp1kJaHGUE8C1e2f4IfG/i0JIvrOatMYuVQZz83pcR1lAB8LJqff7/0Zeu1YuKajwzph73jQ8MybheLwE+g6Jfs+t20Pglv44sfG4f/sZ99ypJ75mXwaeyeG9SwNXqfdTJL+FGrcCwL1obpQjkdPl2h6e2uOUq1i4hoaLHIWSz4Jxut9nJaDF0KH5n05yRQ11iga3JzLPyTNj0hGnXSuX4HvvRQBCB1ddNVcVjQTUSN+G792RAASuvzu8D2sh4CSWI3D9XQD4PngFI2PXsQvbNjFvPhueY5fWHLtuowKKUuTsZR1MQM3FSkCLqsgWLOWrRDkSESnqlIAWdY4DwZxchwwNv426YPvLAcK9cdlZkePGru3EjBqCYYXIuehqAjfdB4C5ehlYoajEetKsEDGvP4mRlUno3LaEOnaLdkS5hNpffnAo7r5wgn+Mobiebz/GvWguTnxJAjc/WMBRipydrLqNcHwxmH+twdi9M9rhyGlwaf6niOQRJaBFlRXCPe9HYh/rTfydXTD/Nqzp8EOiUrSiO+s5lapi1UnDCPiJ7389cQ//k9ghvYl94m5c+/YQanAeOdf3xUlIxC5fGSPgx/XXmmiHfVyeCeMwVy3FLpOE/7b+hW/YqmGEh+LGxOH+dRbuuT8eUcS1cjHe8W8C4O89ACepQkFHKXJ28nixGoTnWpuL50U5GDkdLi1uKCJ5RAloUZMTwP3jV8Q9chMxY4ZhbliFEQri+79nI8MOIw8J/ZYyqnIu64HjcmHs34tr+ybMDStx7UnHLl8Z/12PRYZHW7XDW4cU6mG4mfvxTgzv+RnoMwhKlI5yQEeXayjuuyPx/vdtOLA3fHJfBjGjh2HYNjmXX4/VpE0UIxU5+4QaaR5oUabRVSKSVzRBsCgJhYh96l7M9SuBcA9nzuU9cc//Cfcfv+J78zn8Dz6nh0QhYZ3blszXJ2FkHQB/FoY/CwIB7Br1ci3cY9VJwzNrMubKJdFbUfYE3HOnYuQECNU/F+ucptEO57hCF3Qh+OdveOZOxfvV+3gmf0rwwm64Nq7FlZGOVbtheNsVESlQVqOWAJjLFoanjni8UY5IToVr+yZAQ3BF5MypB7QIcc+chLl+JXbZZPx3PUbWcx8QurAbgTsG4MSXwr1kPp4fvjg8BFcJaPT5YnDKJOFUTMWuXg+7XuMjVo21ajcEDq6Ee5JbiBQox8Hz0zdAOLkr9AyDQN/BZA18hVBaC4yAH+/kT3EvW4hTsjT+u4bAaWyaLCJnxkksh5VSEyPgx1y5ONrhyKmIrK5v4iSVj3Y0IsVSly5deOCBBxg0aBDVqlWjZs2avPbaawQCAR566CFSU1Np2LAhH3/8ceSaLVu2cOutt1K1alWqVq3Kddddx5o1h6d0rVu3juuvv546depQqVIl2rdvz+TJk3O9b1paGiNGjOC+++4jJSWF+vXr88orr+RrW5WAFhWBbLxfvBv+6w13E2p5YWQZdKdsMv5b+wPg/eQ1jF07cAyX5rcVEU7FVJwSpXDt3Y2xc2u0wzmCa/0KzL9W45QoFVm1tyiw6zbC/9Bwsh4fS6hZe+zSZfDfORinrPavE4mWSC/oIs0DLUoiq+snaXV9kfz02WefUaJECaZOncp9993HgAEDuPHGG6lZsyY//fQTPXv25F//+hdbt24lKyuLrl274vP5mDhxIt9//z3ly5ene/fuZGWFF8A8cOAAF110EV988QWzZs2iW7du9OrVi5UrV+Z63zFjxlC/fn2mT59Ov379GDJkCPPnz8+3duqnSBS55/2Ie/YP4cVcDANcLpz4kuT840ac/1lAyDP5M1x7d2PVOAer2QVH1GU1a0ew/eWRbT/s5Irg9hRIO+QMGQZWnTTcv/6MuXIJoUK2eJTnp4kABM+/pEgOmbOr18V/77BohyEihPcD9U78EPeiueTccHe0w5GTpKk9UhwkvLO5QN8v45ZTv1/q1avHgAEDALjnnnt46aWXcLvd9O3bF4BHHnmEl19+mfnz57Nv3z4cx2HMmDGR/ThfeuklatWqxZQpU7jyyitJS0sjLS0tUv9DDz3E5MmT+eqrr+jfv3/keMeOHenduzcAffr0YezYsUyfPp0WLVqcdvuPRwlotDgO3g9ewbU/44hT5pIFZA96JdKDaezbg3fSRwAEevQ55uqjgRvvwVyxCNf2zZqjUcRYtf+WgLa9JNrhHObPwj33BwCCHf4R5WBEpKiza9XHiSuBa9tGjO2btaJqEeHadnD+p/69RPJVgwYNIn83DIPk5ORcxzweDwkJCezcuZPly5ezYcMGqlTJvTdvVlYW69atAyAzM5PnnnuOKVOmsG3bNkKhEH6/P1ed//u+ABUqVGDnzvzbMksJaJQYW//CtT8Du1QZArc8CLYDjo138meYq5cS+9wDZA98BadMEp6v3sfwZxNq3Aq7XpNjVxoTh7/vEGLGPkWoTeeCa4ycMatO4VwJ1z1vGoY/G6t2Q5xKVaMdjogUdaYbq04j3L/Pxly/kpASmiLBtePQFixVTlBSpPA6nR7Jgubx5B69aBgG7v9Zt8IwDGzbxrZt0tLSePvtt4+op0yZMgAMHjyYH374gSeeeIKaNWsSFxfHnXfeSU5Ozgnf18nHdUmUgEaJuTKcaFh1G2Od2zZyPLv+ucQ+9yDmhpXEDH+IwO0P45n2NY7hIue63ies165el6xn38+3uCV/2NXq4Hi8uLZsgP0ZUDIh2iEB4JkeXnxIvZ8iklfsytXg99m4Nq+PdihykozI/uKF/wO8yNmicePGjB8/nrJly5KQcPTPjXPnzqVnz550794dAL/fz7p166hZs2ZBhnoELUIUJeaK8AqAdt1GuU/ElyS7/3CsytUwt6wn9sl7MCyLUNtLsKvUiEKkUiDcHuwa5wBgrloW5WDCXBvXYq75EycunlDzDtEOR0SKCbtyNQBcW9ZHNQ45eS7NARUpdK699lrKlSvHDTfcwKxZs1i/fj0///wzgwYNiqyEW7NmTb755ht+//13li1bRu/evQkEAlGOXAlo1Bxagv7Q0MtcSibgf/h57PKVMWwbx+Ml58pbCjhCKWiFbRiu+1DvZ+uLwBcT5WhEpLiIJKDqAS0agjnh1fVdWl1fpDCJi4tj0qRJVKtWjZtvvpkWLVrQt29fMjIyIj2iTz31FMnJyVx++eVce+21NG/enNatW0c58nwYghsIBHj00Uf5/PPP8fv9tG/fnueff57KlU/ut2bPP/88TzzxBHfccQcjRozI6/AKBWP3Dlzp23Bi47FTjt6r6SQkkv3IC/j+M4pQs/Y4ido6orizah9MQFcWfAJqbP0L32f/BwE/ODY4DuaaP4AisveniBQZdsVUHMPA2L4JQkGt2F7IGTu3YjjOwdX1NXNLJL9MnDjxiGNz5sw54tjft1ApV64cY8aMOWadqampfPXVV7mO3XvvvbleL1ly5OfOo8WSl/K8B3TAgAFMmDCBt956i0mTJrF//3569OiBZVknvHbBggW89957R6zEVNyYKw7O/6zdMLKX59E4ieXx93uS0PkXF1RoEkVWrfo4hoFr3QrIObPhEa71K0++Dsch5q3huH+ZiXvpAtzLfsH9x68YAT9W7YbYVWufUSwiIrn4YnCSKmJYVmRuoRReru0afisieStPf5W1d+9ePvjgA0aPHs2FF14IwNixY0lLS+Onn36iU6dOx732jjvuYNSoUQwfPjwvwyp0jjv8Vs5e8SWxq9TA3LiGmFcfC2/2nRMAK0SoVadwT+QxtuD5O/eMScS8NRyrSg38Dz6HUzb5+OXn/Yi5aml4RebbHg6/r8sFLhdWtTp51ToRkQi7clVcO7fg2rwe6+CQXCmcXFqASETyWJ72gP7+++8Eg0E6duwYOValShXq1q3LvHnzjnvtfffdR/fu3bngggvyMqRCyRVJQBudoKScbaz65wLgXjQX96+zwj2Sf/5GzDsj8b0zMjxc7bgVhPB+/R8AzE1rw4tYbdlw7PKBbLyfvA5AzjW3YzVpjZXWHKvBeVjnNIXY+Dxpl4jI39mVqgGaB1oUGJEtWJSAikjeyNMe0B07dmCaJomJibmOJycns2PHjmNe995777F27VrGjh2bl+EUTgf2YW5ah+P2YFevG+1opJDJufLmyJBXxxcDXh9G+jZ8H47GM30irq1/4b93GE6pMke93r1wBq6dW7CTK+GULoO5ehlxT95L9gPPYNc6cmi7d+JHuHbvxKpah1C7S/O1bSIih2ghoqLDtW0TALb2ABWRPHJSCeiTTz7JyJEjj1tmwoQJxzznOA7GMYYOrlq1imHDhvHtt9/i9XpPJpxc1+anI+q3beK2rKP0ykWUWrsMDIN91euzv2YDDlSpGR66eAKlVi6iBJBZsSqrNvyVP4FL0Vaueu7XKWWJ7dWfGp+NxrtyCZ5Bt7H2urvJrpCau5zjUPfzdwDY1LwTu9NaUv2/b1B61WJinrmfDd1uJuOcZpFhvN6MdM6Z+BEAazpcSeaatfnetEPy+94VOVsVlXsr1nJRDwitX1lkYj5b1d+8Hjewzh8icBb/W+n/adERExODz+eLdhhnjX379h21o7F27WOvIXJSCWjfvn257rrrjlumSpUqLFiwAMuy2LVrF0lJSZFz6enptGnT5qjXzZ8/n127duVaEtiyLGbPns3bb7/Nli1bjvmf6HgNO1OrVq06XH92Fr5PXsNcOBPX/oxc5eK2bqDC7G9xYuKwajXAiS8JMbE4MXE4pRIIdvgHlCgdKe/99cfwn41b5mv8UszUrk2w8bmYrwzGu+YP6v7nebIHv5prb1hzyQJit2/ELl2Gslf+k7JeH9R9geC7L+CZMYnq/30Dq8ZMcq64GatRC2JG/wdXKEiwVScqdbyswJqS694SkTxTpO6t1CrwNsTs3kHt6tW1umphFQri3bsbx3CRel5L8JxaR0FxUaTuLWHv3r3ExGj7uIJSqlQpUlJSTumak/qJn5iYeMSw2qNp0qQJHo+HadOmce211wKwefNmVqxYQcuWLY96TZcuXWjatGmuY3fffTc1a9bkgQceOOVe0fzg+/BVPDMmAWAnVSDUtA1W43DCbC6Zj7lkAeaW9biXLjjiWvcvs8geNCrycDU1/1NOk5OQSPaAl4h5/UncC2cQ8+JAsh97LTIc1zPxQwCCl1wL3oO/tDHdBG7tj51aC89X72Ou/ZPYFx7BSqmJuXENjtdHznV9otUkETlb+WKxkyrgSt+GsWMzTqWq0Y5IjsJI34bh2NhJFc7a5FNE8l6e/sqxdOnS9OrViyFDhpCcnEyZMmUYNGgQDRo0oEOHDpFyzZs354477qB3794kJCRENks9JC4ujjJlylC/fv28DO+0mEsW4JkxCcfjIfuRF8Pz6P42nNhKaw6AsWsHrr9WY/izwJ+N4c/C893nmGv/xPv5W+T06AM5AVzrVuAYBlbt4r3VjOQTjxd/n0HE7tqBuW45Ma8MJvuRF3D9tQb3n7/hxMYTvLBb7msMg+BFVxFsfxmeqV/hmfQx5sY1AOT840btMSsiUWFXroYrfVt4JVwloIWSa2N4aobmf4pIXsrzMS9PP/00pmlyyy234Pf7ad++Pa+//jqmeXi/y1WrVrFr1668fuu8l50VXnkUyLniZuzaDY9Z1Eksh/U/H+StmvWJfaYf3kkfYdVvCm4PhhXCSq0FcSXyNXQpxrw+/Pc9RezQOzFXLcX39kiMQDYAwY7djv1/yxdL8PKeBDt1x/Pj1xgZuwhe1qMAAxcROcyuXA0WzcW1ZQMn3ilcosG9OLyDgXVOkyhHIiLFSZ4noDExMYwYMYIRI0Ycs0xGRsYxzwFMnDgxr8M6Ld7P3sC1aztWtTqn9UHdrpNGzlW34hv/Jr6xTxNq0QEAq66G38qZcRIS8d/3NLFP3otn9nfhY24PwYuvOfHFvlglniISdfbBXk/X5nVHntyfAbElNDc0mmwbc9EcgMi0IxHJP3379mX37t188skn0Q4l3xX7n+zmgp+IeXskjseLU6IUlCiNU7I0wfaXYzVudczrSmxYgXfqlzimSeC2R05qhdujCXa5HvOPX3H/8SveqV8Cmv8pecOuWhv/nYOIGTUEw3EItb0UJ+HEc7VFRAoDu3J4xW/X5tx7FRs7thA35A6cuBL4+z0Z2ZpKCpZr3Qpce/dgJ5bHTqlx4gtERE6SK9oB5KvM/fjefxkj6wCuvbsxN6/HXLEovIDLSwMxF848+nUBP6nfvAdAsOs/sVNrnn4MLpNA74HYJQ/Pc7XrpJ1+fSJ/Y53XjsBN92HVrE9Ot39GOxwRkZNmVwxvJeXathGsUOS454cvMLIzce3aTuyT92IumB6tEM9q7t9nAxBq0jrX2hcicnYIBoP5VnexTkC9X76La98erDppZL74KVlPvEn2Iy+Qc/HVGLZNzGvDMJfkXrnW2LubmFcfw7dnJ1aV6uR0PfMP9U6ZJAK9BwBgVamhXirJU6GO3ckeMgYnsXy0QxEROXmxcdiJ5TFCQYwdW8LHAtl4ZoZXnQ+lNcfI8RP76mN4vngXbDt6sZ6FzIMJqNX06NvoiUj+CQQC/Pvf/6Z27dqUL1+ezp07M2fOnMj5Tp068dJLL0Ve33HHHSQkJLB9+3YAsrKySE5OZu7cuQA4jsPLL79MkyZNqFChAm3atMk11HfDhg0kJCQwfvx4unbtSoUKFXjnnXfyrX1FOgE19u4+5jnXxrV4fvgCx3AR6NUPp2w57NRaWPXPJeeGe8i56GqMUJCYVx7FdXBrFHPBdOIG3YJ78TxCvlgCdwwAtydPYrUatSRr2P/hf+DZPKlPRESkqLMrVwMOD8N1z/4eIysTq1YD/A8OJ9CzL47hwvflu8SMfhz2HX8NCckbxq4dmH+twfHFYNVtHO1wRM46Q4YM4YsvvuDVV19lxowZ1K9fn2uuuYZt27YB0LZtW2bOPDyS8+effyYxMZFZs2YBMG/ePDweD+eddx4ATz75JB988AEjR45k7ty53H///dx///1MmTIl1/sOHTqU22+/nblz59KlS5d8a1+RngMa/6+rsCpXI9T2UoKXXHN4nqbj4PvPyxi2TU7nK7FTa+W+0DDIueFujEA2nhmTiH1hAFaD83AvnAFAqMF5LO94HdWq1cnTeDWPRURE5DC7UlVYPA/X5nVY57XF88MXAAQ7XxXeQuqyHtiVqhHz2jDcC2cQ/+fvBHr0IdTuMnAd53fojgOZ+yEmTgsZnQbz94OLDzVsfnhfaZEirsT/61Cg73fgvZ/obq2pAAAZtElEQVRO67rMzEzefvttXnnlFS655BIAXnzxRWbMmMGbb77Jo48+Stu2bXnzzTcJhUJs2LCBffv20adPH2bOnMnVV1/NrFmzaNGiBR6Ph8zMTEaPHs1///tf2rQJj2ioVq0av/zyC2+++WbkPQB69+5N9+7dz7jtJ1Kkfyo7Xl94Xucnr+NeOAN/n4E45avgnvcj5vJFOCVLk3PVrUe/2OUicMuD4eE+86bhXjgDx+sjp8edBDt2J7hmTcE2RkRE5CwTWYhoywZcKxZhblqHXbosoebtI2Wsxi3JGvoGvvdexL1sITFvj8CaNYVAr3/heLy4dmzFSN+Ka8cWXOnbMHZswbVzK0Z2Jna5SmQ9837hS0Idp1DPqzw8/1PDb0UK2rp16wgGg7RqdXixVNM0adGiBcuXLwegdevWBAIBfv31V/78809at27NBRdcwAMPPADArFmzuOiiiwBYsWIFfr+fa665BuNvP3eCwSCpqam53rtp06b53TygiCegmWMmYC5ZgO/9FzHX/EHco7eTc+0deCZ+BEDg2t4QX/LYFbhMAr0HgS8WY+9uAjfcjVMhpYCiFxERObvZlQ9uxbJlPd6DvZ+hC7seMf3FKV8Zf/8RuOdOxfvhaMyVi4kbfPsJ63ft2IJr4xrs6nXzPvjT5Nq0jtin+xFq1o7ALQ8VvkQ0kI355684hoHVuGW0oxHJM6fbI1nQHMcByJUsHnLoWIkSJWjcuDEzZ85k+fLltGvXjhYtWrBx40bWrFnDr7/+ytChQwGwD86f/+ijj0hJyZ3nuP/nl3Px8fF53p6jKdIJKB4v1rnnk1W3Eb4PXsYz5wd840YBYFWvFx6icyJuN4HbHs7nQEVEROR/Hd4LdANsWodjmgQ7dD16YcMg1LozoUYt8X32Bu45U3FKlsZOroiTXBE7uRJOuYrYSRWxy1XE99FreH6egrl6WaFKQL0fj8HI3Idn+kSckgnkXHtHtEPKxVz2C0YwiFXzHJzSZaMdjshZp0aNGni9XubMmUO1atUAsCyL+fPnc801h/d7PzQPdOXKlfTt25eYmBjOO+88Ro4cmWv+Z926dfH5fGzcuJELLrggGk06QtFOQA+JL0ngzkexmrbB996L4M8m0Kvf8eeHiIiISHTFxmOXLYdr9w4Agi0vxCmTdPxr4ksSuPlBAjc/eNxiVu0GeH6egmv1MrjoqryK+IyYS+bjXrIAxxcDwRy834zDTixHqGP+z7k6We7fNPxWJJri4+O59dZbGTp0KImJiVStWpUxY8awc+dObr/98MiPtm3b8uqrrxIfH0/jxo0jx55//nnatWuHxxMeSVKyZEnuvfdeBg8ejOM4nH/++Rw4cICFCxficrm4+eabC7yNxSMBPSjUsiOhhs0xMvfjlKsU7XBERETkBOzKVQ8noJ3zLlG0azUEwFy9NM/qPCO2hffj1wHIueJmnPiSxLw9At/7L+OUSS4c253YNuaigwsQKQEViZpDw2fvvvtu9u7dS6NGjRg/fjwVKlSIlGndujWGYdC6dWtM0wSgXbt2DB8+nLZt2+aqb9CgQSQnJ/Pqq6/y4IMPUrJkSdLS0ujXr1/BNepvilUCCkB8SZzjzfsUERGRQsOuXB2WLMBKrYVdu2Ee1lsVJzYeV/p2jD3pJ+5ZzWfuWVMwN63FTipPsPOV4PWRs2sH3q/eI2bMMLIHvIRdo17evJk/C/OPXzFXLoGcAEYoCFYIQiGMg3+GXwfBF4tdMQW7QgoYLlx792AnlsdOqZE3sYjISXnttdcif/f5fDz77LM8++yxt28sUaIE6enpuY61a9eOjIwjt6syDIM+ffrQp0+fo9ZVtWrVo16XX4pfAioiIiJFRqhVJ9yL5pBzXZ+8XZDHZWLVrI976QJcq5dhNY/i3KdANt7P3wIg55o7Ilub5Fx5M8au7XhmTSb2mfsIduhC8NIeOInlcl/vOBi7d0IgG+NQ8miFwLLCCeXBL9eOLZi/z8VcsSicdJ6s33K/DDVpXfgWRxKRYkMJqIiIiESNXb0uWc9+kD9116oPSxdgRjkB9Xz7Ka6MXVjV6xJq2fHwCcMIr4RrhfDM+QHvd5/jmfoVoTYXEWrdGdfmdZgrl+BauRjX3j0n/X6OYWDVrI/VsDlOqQQc0x3eisZ047g9YJrhlYZNN2QdwLX1r8iXkZ1J6MJu+fBdEBEJUwIqIiIixZJ1aB7oqgKeB2pbkHUA48B+jIx0vJMObg/Xs++RCyS63QTufJTg5T3xfPMh7vk/4Zn5LZ6Z3+Yq5pQsjVOidDiZNN3gNsMJpekGlwluN058KayGzQg1agElE046XOuMGywicvKUgIqIiEixZNU8B8cwcK1fCTmByNDXvHuDEN7xb+LauCacbGbuwziwDyPrwBFFQ+eej12vyTGrslNrEbhrCDlX34p30ie41v6BnVoLq04jrLqNcMpX0bBYESkWlICKiIhI8RRXArtydcxNa3FtWJWnixwBuBdMxzvp46Oec+JK4MSXwilREichicAN95xUnU75KgRuOf4WMyIiRZkSUBERESm27NoNMDetxVy1NG8TUMfBM2U8ADld/0moaZtIwklcifCwWBEROYISUBERESm2rFoN8EybgLl6GcdbF9bYtgnPtK/B7SHY4R84yRWPW69r9TLMtX/ixJcip+s/wReTt4GLiBRTSkBFRESk2Dq0EJFr9VJwnCPmUbr+WoPnm//gnj8dw7EB8Ez8CKtpG4IXX41Vr8lR5156p3wGQPDCrko+RUROgRJQERERKbac8pVxSpbGtXcPxs6tOOUqAWBk7ML3zvO4f58dLme6CZ5/KYRCuOf9iPvXWbh/nYVVrQ7++57GKZMUqdNI34a5cCaOaRLsdEVU2iUiUlQpARUREZHiyzCwajXE/dvPmKuXESpXCQ7sI2bEQ5ib1uF4fQQ7/IPgpT1wEssBkNOjD+5pE/BM+wpz/UpiXvg32QNfgdg4ADzf/xfDsQm26IxTNjmarRMRKXJcJy4iIiIiUnRZteoD4XmbZGcR+/wjmJvWYVdMJWv4OHJuvDeSfAI4CYkEr7yZrKfewS5fBfOv1cSMfhysEGRn4Zk+EYDgJddGozkiIkWaElAREREp1g7NAzX//J2Ylwdhrv0TO6kC2Q+PzDW09gglE8h+8FmcEqVwL5mP7/2X8cz8FiM7E6tOGnb1ugXUAhGR6LBtG8uy8rROJaAiIiJSrNnV6+KYJuaW9bj//A07IZHsh5/HKVvuhNc65auQfd/TOB4Pnp8m4P3sDQBy1PspInmoS5cu9O/fP9exvn370qNHj8j5+++/n0ceeYSqVatStWpVBg8ejG3bkfJpaWk888wz9O7dm8qVK1OnTh1GjRqVq869e/fSr18/atWqRZUqVbj88sv57bffIufHjRtH5cqV+e6772jdujXJycmsWLEiT9uqBFRERESKN18MdmptAJz4Uvj7j8QpX/mkL7drN8TfZxCOYWDkBLCTK2Kde35+RSsiclSfffYZtm3z/fff89JLL/Hee+8xZsyYXGXGjBlDnTp1mD59OgMGDGDYsGF8/fXXADiOQ48ePdi6dSuffPIJM2bMoE2bNnTr1o1t27ZF6vD7/YwcOZIXX3yRefPmkZKSkqft0CJEIiIiUuwFL7oKpowncPMD2FWqn/L1VvMO5NyQjvfDMeR0uwlcZj5EKSL5JfPHSwv0/eI7Ts7zOsuXL8/w4cMxDIM6deqwevVqxowZwz333BMpc9555/HQQw8BUKtWLX799VfGjBlDt27dmDFjBkuWLGH16tXExsYC8OijjzJ58mQ++eQT+vXrB4BlWQwfPpwmTZrkeRtACaiIiIicBULnX0zo/IvPqI7gxdcQ7Ngd3J48ikpE5OQ1a9YM42/7Erdo0YKnnnqKffv2UapUKQCaN2+e65rmzZszYcIEABYtWkRWVha1atXKVcbv97Nu3brIa7fbTVpaWn41QwmoiIiIyElT8ilSJOVHj2RecrlcOI6T61goFMrT97Btm3LlyvHtt98eca5kyZKRv/t8Pkwz/0Z5KAEVERERERGJoqSkpFzzMAGWLl1Kampq5PUvv/yC4ziRXtAFCxZQsWLFSO8nwMKFC3PVsXDhQurWDa/Y3bhxY3bs2IHL5aJatWr51JIT0yJEIiIiIiIiUdS+fXt++OEHJk2axKpVqxg4cCCbN2/OVWbbtm38+9//ZtWqVXz11Ve88sor3HXXXbnKLFy4kBdeeIE1a9bw3nvv8fHHH0fKdOjQgVatWnHDDTfw/fffs379eubPn8/TTz/N7NmzC6yt6gEVERERERGJon/+858sW7YssqDQbbfdRpcuXdi9e3ekzLXXXott23Tq1AnDMOjVq9cRCehdd93FsmXLeP7554mLi2PgwIF0794dAMMw+PTTT3nyySfp168fO3fupFy5crRs2ZLrr7++wNpqZGRkOCcudvZZtWoVtWvXjnYYIsWO7i2R/KF7SyR/6N4qWvbu3Uvp0qWjHUae69KlC/Xr12fEiBHHLJOWlkbv3r259957Cyyu0/l+awiuiIiIiIiIFAgloCIiIiIiIlIgNAdURERERESkEJs4ceIJyyxZsqQAIjlz6gEVERERERGRAqEEVERERERERAqEElAREREREREpEEpARURERESkWHC73WRmZuI42mkyPzmOQ2ZmJm73qS8ppEWIRERERESkWIiPjycQCLBv375oh1LsxcTE4PP5Tvk6JaAiIiIiIlJs+Hy+00qMpGBoCK6IiIiIiIgUCCWgIiIiIiIiUiCUgIqIiIiIiEiBUAIqIiIiIiIiBcLIyMjQGsUiIiIiIiKS79QDKiIiIiIiIgVCCaiIiIiIiIgUCCWgIiIiIiIiUiCUgIqIiIiIiEiBUAIqIiIiIiIiBaLYJqA///wzPXv25JxzziEhIYFx48blOn/gwAH69+9P/fr1qVChAs2aNWP06NGR83v27KF///40b96cChUq0KBBAx544AF2796dq56MjAx69+5Namoqqamp9O7dm4yMjAJpo0g0nOm9tWHDBhISEo769corr0TKBQIB+vfvT40aNahUqRI9e/Zk8+bNBdZOkYJ2ontrx44d9O3bl3r16lGxYkWuvvpq1qxZEzmv55bI0Z3pvaXnlkjeKrYJaGZmJvXr1+fZZ58lNjb2iPODBg3iu+++4/XXX2fevHk8+OCDDB06lI8//hiArVu3snXrVoYOHcrs2bMZO3Yss2fP5rbbbstVz+23387ixYv57LPPGD9+PIsXL6ZPnz4F0kaRaDjTe6tKlSqsWLEi19fzzz+PYRh069YtUs+AAQOYMGECb731FpMmTWL//v306NEDy7IKrK0iBel495bjONx4442sXbuWcePGMWPGDFJSUujevTuZmZmAnlsix3Km95aeWyJ566zYB7Ry5coMHz6cG2+8MXKsdevWdO3alYEDB0aOXX755TRo0IARI0YctZ7vvvuOHj16sGHDBkqVKsWKFSto2bIlkydPplWrVgDMmTOHyy67jAULFlC7du38bZhIlOXVvXXFFVdgGAZffPEFAHv37qVWrVqMHj2a6667DoBNmzaRlpbG+PHj6dSpUz62SiT6/vfeWr16Nc2aNWPmzJmkpaUBYNs2derUYciQIdx0001HrUfPLZHc8ure0nNL5PQV2x7QE2nVqhWTJ09m06ZNAMybN4+lS5ce9wfE/v378fl8xMXFATB//nxKlChBy5Ytc9UbHx/PvHnz8rcBIoXUqd5b69evZ/r06dx8882RY7///jvBYJCOHTtGjlWpUoW6devq3pKzUiAQACAmJiZyzOVy4fP5mDNnzjGv03NL5PhO597Sc0vkzJy1Cehzzz1HWloaDRs2JCkpiS5duvD4449z6aWXHrV8RkYGTz31FDfddBNutxsIzxlITEzEMIxIOcMwSEpKYseOHQXSDpHC5lTvrffff5/ExEQuv/zyyLEdO3ZgmiaJiYm5yiYnJ+vekrNSnTp1SElJYdiwYezZs4ecnBxeeuklNm/ezPbt2496jZ5bIid2OveWnlsiZ8Yd7QCiZezYscybN4+PPvqIlJQUZs+ezeDBg0lNTaVz5865ymZmZnL99ddTsWJFhg0bluvc3x/ihziOc9TjImeDU7m3QqEQH374ITfccAMej+eEdevekrOVx+Phgw8+4J577qF69eqYpkmHDh246KKLjlpezy2Rk3Oq95aeWyJn7qxMQLOzsxk2bBjvvvsul112GQANGzZkyZIljBo1KteH5AMHDnDttdcC8Mknn+QaolGuXDnS09Nz/XBxHIddu3aRnJxcgC0SKRxO5d4C+Pbbb9m2bdsRc2zKlSuHZVns2rWLpKSkyPH09HTatGmT/w0RKYSaNGnCrFmz2Lt3L8FgkKSkJDp16kTTpk1zldNzS+TUnOy9BXpuieSFs3IIbjAYJBgMYppmruOmaWLbduT1/v37ueaaa7Btm08//ZQSJUrkKt+iRQsOHDjA/PnzI8fmz59PZmZmrvk1ImeLk723Dnn//fc5//zzqVWrVq7jTZo0wePxMG3atMixzZs3RxZQETmblS5dmqSkJNasWcNvv/2Waxignlsip+9499Yhem6JnLli2wN64MAB1q5dC4RXM9u0aROLFy+mTJkypKSkcP755zN06FDi4+NJSUnh559/5uOPP2bo0KFA+CF+1VVXsX//fsaNG0dWVhZZWVkAlClTBq/XS926dencuTP3338/L7/8Mo7jcP/993PJJZdoJUEpts703jpk48aNTJ06lddff/2I9yhdujS9evViyJAhJCcnU6ZMGQYNGkSDBg3o0KFDQTRTpMCd6N768ssvKVu2LKmpqSxbtox///vfdOnSJbLoiZ5bIkd3pvfWIXpuieSNYrsNy8yZM+natesRx6+//npee+01tm/fztChQ5k2bRp79uwhJSWFm266iXvuuQfDMI55PcCECRNo164dEN74+5FHHuHbb78F4LLLLmP48OEkJCTkX+NEouhM761Dnn76ad544w2WL1+ea4jgIX6/n8GDBzN+/Hj8fj/t27fn+eefp0qVKvnaPpFoOdG99frrrzNq1Ch27NhB+fLl6dmzJw8//DBer/e414OeW3J2O9N76xA9t0TyRrFNQEVERERERKRwOSvngIqIiIiIiEjBUwIqIiIiIiIiBUIJqIiIiIiIiBQIJaAiIiIiIiJSIJSAioiIiIiISIFQAioiIiIiIiIFQgmoiIhIPhg3bhwJCQls2LAh2qGIiIgUGkpARURECpHJkyfzzDPPRDsMERGRfKEEVEREpBCZMmUKzz33XLTDEBERyRdKQEVERERERKRAKAEVERE5QwsWLODiiy+mfPnyNGzYkBdffBHHcXKVmTRpEj169OCcc86hXLlyNGzYkMcee4xAIBAp07dvX9555x0AEhISIl9/n0f6+eef06lTJypWrEhqaio9evRg+fLlBdNQERGRM+SOdgAiIiJF2fLly7niiisoWbIkDz30EF6vl3fffZf4+Phc5f7zn/9gmia9e/cmISGBefPmMWrUKDZv3sybb74JwC233MLmzZuZMWMGY8eOjVyblJQEwEsvvcTjjz9O165d6dmzJ5mZmbz55ptccsklTJ8+nWrVqhVYu0VERE6HkZGR4Zy4mIiIiBxNr169mDx5MvPnz6d69eoApKenc+6557Jv3z4WLVpE1apVycrKIi4uLte1I0aM4Omnn2bp0qVUrlwZgPvvv5933nmHjIyMXGU3btxI06ZNefDBBxkwYEDk+LZt22jRogXdunXj1VdfzefWioiInBkNwRURETlNlmUxdepULr300kjyCeEey+uuuy5X2UPJp23b7N27l127dtGmTRscx2HRokUnfK8JEyYQCoW4+uqr2bVrV+TL4/HQrFkzZsyYkbeNExERyQcagisiInKa0tPTycrKonbt2kecq1WrVq7Xf/75J0OGDGHWrFlkZ2fnOrd3794TvteaNWsAaNGixVHP/2/vqoiISGGkBFREROQ0HVpoyDCMY56DcILZtWtXYmNjGTx4MNWrVyc2NpYtW7Zw1113Ydv2Cd/rUJnx48fjdh/5+Ha5NKhJREQKPyWgIiIipyk5OZm4uDhWrlx5xLlDPZYAM2fOJD09nW+++Ya2bdtGjk+bNu2I646WzAKRIb5VqlShXr16Zxq6iIhIVOjXpSIiIqfJNE06duzI5MmTWbduXeR4eno6n332Wa5ykLtX1LZtRo8efUSdh4bS/u8iRN26dcPtdvPMM88ctcc0PT39zBojIiJSANQDKiIicgYGDhzIjz/+yGWXXcbtt9+Ox+Ph3XffJSUlJTK3s1WrVpQtW5a+ffvSp08f3G43X3/9NQcOHDiivqZNmwLQv39/OnfujNvt5tJLL6VatWoMHTqUQYMG0blzZ7p27UqZMmXYuHEj3333Hc2aNePFF18s0LaLiIicKm3DIiIicobmzZvHo48+yuLFi0lOTua2224jOTmZe+65J7INy8KFCyNl4uPj6datG7feeivnn38+o0eP5sYbbwTCK+sOHDiQL774gp07d0ZWya1atSoAU6ZMYdSoUSxatIhQKETFihVp1aoVt99+O+eee240vw0iIiInpARURERERERECoTmgIqIiIiIiEiBUAIqIiIiIiIiBUIJqIiIiIiIiBQIJaAiIiIiIiJSIJSAioiIiIiISIFQAioiIiIiIiIFQgmoiIiIiIiIFAgloCIiIiIiIlIglICKiIiIiIhIgVACKiIiIiIiIgXi/wN3UluzhwQuLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_ci.plot(lw=2, figsize=(14, 8));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kelly Rule for a Single Asset - Index Returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a financial market context, both outcomes and alternatives are more complex, but the Kelly rule logic does still apply. It was made popular by Ed Thorp, who first applied it profitably to gambling (described in Beat the Dealer) and later started the successful hedge fund Princeton/Newport Partners.\n",
    "\n",
    "With continuous outcomes, the growth rate of capital is defined by an integrate over the probability distribution of the different returns that can be optimized numerically.\n",
    "We can solve this expression (see book) for the optimal f* using the `scipy.optimize` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:49.129611Z",
     "start_time": "2018-10-30T23:49:49.125388Z"
    }
   },
   "outputs": [],
   "source": [
    "def norm_integral(f, mean, std):\n",
    "    val, er = quad(lambda s: np.log(1 + f * s) * norm.pdf(s, mean, std), \n",
    "                               mean - 3 * std, \n",
    "                               mean + 3 * std)\n",
    "    return -val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:49.296104Z",
     "start_time": "2018-10-30T23:49:49.290769Z"
    }
   },
   "outputs": [],
   "source": [
    "def norm_dev_integral(f, mean, std):\n",
    "    val, er = quad(lambda s: (s / (1 + f * s)) * norm.pdf(s, mean, std), m-3*std, mean+3*std)\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:49:49.401152Z",
     "start_time": "2018-10-30T23:49:49.397658Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_kelly_share(data):\n",
    "    solution = minimize_scalar(norm_integral, \n",
    "                        args=(data['mean'], data['std']), \n",
    "                        bounds=[0, 2], \n",
    "                        method='bounded') \n",
    "    return solution.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:02.646781Z",
     "start_time": "2018-10-30T23:49:50.080279Z"
    }
   },
   "outputs": [],
   "source": [
    "annual_returns['f'] = return_params.apply(get_kelly_share, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:02.965967Z",
     "start_time": "2018-10-30T23:50:02.648058Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_params.plot(subplots=True, lw=2, figsize=(14, 8));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:02.972487Z",
     "start_time": "2018-10-30T23:50:02.966989Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sp500</th>\n",
       "      <th>f</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>0.113906</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>-0.007266</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>0.095350</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.194200</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>0.014815</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               sp500         f\n",
       "date                          \n",
       "2014-12-31  0.113906  1.999996\n",
       "2015-12-31 -0.007266  1.999996\n",
       "2016-12-31  0.095350  1.999996\n",
       "2017-12-31  0.194200  1.999996\n",
       "2018-12-31  0.014815  1.999996"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_returns.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:03.197070Z",
     "start_time": "2018-10-30T23:50:02.973933Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(annual_returns[['sp500']]\n",
    " .assign(kelly=annual_returns.sp500.mul(annual_returns.f.shift()))\n",
    " .dropna()\n",
    " .loc['1900':]\n",
    " .add(1)\n",
    " .cumprod()\n",
    " .sub(1)\n",
    " .plot(lw=2));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:03.204895Z",
     "start_time": "2018-10-30T23:50:03.198627Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    205.000000\n",
       "mean       1.303795\n",
       "std        0.585540\n",
       "min        0.000003\n",
       "25%        0.830339\n",
       "50%        1.227349\n",
       "75%        1.999996\n",
       "max        1.999996\n",
       "Name: f, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_returns.f.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:03.219089Z",
     "start_time": "2018-10-30T23:50:03.206149Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1814-12-31</th>\n",
       "      <td>0.074059</td>\n",
       "      <td>-0.426468</td>\n",
       "      <td>0.574586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1815-12-31</th>\n",
       "      <td>0.070621</td>\n",
       "      <td>-0.429199</td>\n",
       "      <td>0.570442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1816-12-31</th>\n",
       "      <td>0.064872</td>\n",
       "      <td>-0.436591</td>\n",
       "      <td>0.566336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1817-12-31</th>\n",
       "      <td>0.075920</td>\n",
       "      <td>-0.418596</td>\n",
       "      <td>0.570436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1818-12-31</th>\n",
       "      <td>0.074465</td>\n",
       "      <td>-0.419380</td>\n",
       "      <td>0.568309</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                mean     lower     upper\n",
       "date                                    \n",
       "1814-12-31  0.074059 -0.426468  0.574586\n",
       "1815-12-31  0.070621 -0.429199  0.570442\n",
       "1816-12-31  0.064872 -0.436591  0.566336\n",
       "1817-12-31  0.075920 -0.418596  0.570436\n",
       "1818-12-31  0.074465 -0.419380  0.568309"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_ci.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Kelly Fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:34.086697Z",
     "start_time": "2018-10-30T23:50:34.084711Z"
    }
   },
   "outputs": [],
   "source": [
    "m = .058\n",
    "s = .216"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:43.145919Z",
     "start_time": "2018-10-30T23:50:43.089663Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal Kelly fraction: 1.1974\n"
     ]
    }
   ],
   "source": [
    "# Option 1: minimize the expectation integral\n",
    "sol = minimize_scalar(norm_integral, args=(m, s), bounds=[0., 2.], method='bounded')\n",
    "print('Optimal Kelly fraction: {:.4f}'.format(sol.x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:50:46.455040Z",
     "start_time": "2018-10-30T23:50:46.416441Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal Kelly fraction: 1.1974\n"
     ]
    }
   ],
   "source": [
    "# Option 2: take the derivative of the expectation and make it null\n",
    "x0 = newton(norm_dev_integral, .1, args=(m, s))\n",
    "print('Optimal Kelly fraction: {:.4f}'.format(x0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kelly Rule for Multiple Assets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use an example with various equities. [E. Chan (2008)](https://www.amazon.com/Quantitative-Trading-Build-Algorithmic-Business/dp/0470284889) illustrates how to arrive at a multi-asset application of the Kelly Rule, and that the result is equivalent to the (potentially levered) maximum Sharpe ratio portfolio from the mean-variance optimization. \n",
    "\n",
    "The computation involves the dot product of the precision matrix, which is the inverse of the covariance matrix, and the return matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:55:56.634785Z",
     "start_time": "2018-10-30T23:55:52.556676Z"
    }
   },
   "outputs": [],
   "source": [
    "with pd.HDFStore('../../data/assets.h5') as store:\n",
    "    sp500_stocks = store['sp500/stocks'].index \n",
    "    prices = store['quandl/wiki/prices'].adj_close.unstack('ticker').filter(sp500_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:55:56.650603Z",
     "start_time": "2018-10-30T23:55:56.636164Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 14277 entries, 1962-01-02 to 2018-03-27\n",
      "Columns: 501 entries, MMM to ZTS\n",
      "dtypes: float64(501)\n",
      "memory usage: 54.7 MB\n"
     ]
    }
   ],
   "source": [
    "prices.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:55:56.701358Z",
     "start_time": "2018-10-30T23:55:56.651593Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 359 entries, 1988-02-29 to 2017-12-31\n",
      "Freq: M\n",
      "Columns: 217 entries, MMM to XRX\n",
      "dtypes: float64(217)\n",
      "memory usage: 611.4 KB\n"
     ]
    }
   ],
   "source": [
    "monthly_returns = prices.loc['1988':'2017'].resample('M').last().pct_change().dropna(how='all').dropna(axis=1)\n",
    "stocks = monthly_returns.columns\n",
    "monthly_returns.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Precision Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:55:58.060193Z",
     "start_time": "2018-10-30T23:55:58.019717Z"
    }
   },
   "outputs": [],
   "source": [
    "cov = monthly_returns.cov()\n",
    "precision_matrix = pd.DataFrame(inv(cov), index=stocks, columns=stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:55:58.292542Z",
     "start_time": "2018-10-30T23:55:58.278414Z"
    }
   },
   "outputs": [],
   "source": [
    "kelly_allocation = monthly_returns.mean().dot(precision_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:56:10.805685Z",
     "start_time": "2018-10-30T23:56:10.797766Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    217.000000\n",
       "mean       0.213979\n",
       "std        3.493734\n",
       "min      -10.840354\n",
       "25%       -1.845360\n",
       "50%        0.002192\n",
       "75%        1.990041\n",
       "max       11.316506\n",
       "dtype: float64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kelly_allocation.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-10-30T23:56:13.013799Z",
     "start_time": "2018-10-30T23:56:13.010909Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "46.433472367624404"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kelly_allocation.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Largest Portfolio Allocation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows the tickers that receive an allocation weight > 5x their value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kelly_allocation[kelly_allocation.abs()>5].sort_values(ascending=False).plot.barh(figsize=(8, 10))\n",
    "plt.yticks(fontsize=12)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance vs SP500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kelly rule does really well. But it has also been computed from historical data.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = monthly_returns.loc['2010':].mul(kelly_allocation.div(kelly_allocation.sum())).sum(1).to_frame('Kelly').add(1).cumprod().sub(1).plot();\n",
    "sp500.loc[monthly_returns.loc['2010':].index].pct_change().add(1).cumprod().sub(1).to_frame('SP500').plot(ax=ax, legend=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
